<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3-mathml3.dtd">
<article xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dtd-version="1.3" article-type="research-article">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Vet. Sci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Veterinary Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Vet. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2297-1769</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fvets.2025.1658248</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Bayesian spatiotemporal evaluation of bovine anaplasmosis seroprevalence in Missouri (2010&#x02013;2021)</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Raghavan</surname> <given-names>Ram K.</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Investigation" vocab-term-identifier="https://credit.niso.org/contributor-roles/investigation/">Investigation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Validation" vocab-term-identifier="https://credit.niso.org/contributor-roles/validation/">Validation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Visualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/visualization/">Visualization</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Funding acquisition" vocab-term-identifier="https://credit.niso.org/contributor-roles/funding-acquisition/">Funding acquisition</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Formal analysis" vocab-term-identifier="https://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Data curation" vocab-term-identifier="https://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Resources" vocab-term-identifier="https://credit.niso.org/contributor-roles/resources/">Resources</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Project administration" vocab-term-identifier="https://credit.niso.org/contributor-roles/project-administration/">Project administration</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Software" vocab-term-identifier="https://credit.niso.org/contributor-roles/software/">Software</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &amp; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-review-editing/">Writing &#x2013; review &#x00026; editing</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
<uri xlink:href="https://loop.frontiersin.org/people/2263652"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Ierardi</surname> <given-names>Rosalie</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Data curation" vocab-term-identifier="https://credit.niso.org/contributor-roles/data-curation/">Data curation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Visualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/visualization/">Visualization</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Investigation" vocab-term-identifier="https://credit.niso.org/contributor-roles/investigation/">Investigation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &amp; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-review-editing/">Writing &#x2013; review &#x00026; editing</role>
<uri xlink:href="https://loop.frontiersin.org/people/3208761"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Osei</surname> <given-names>Frank Badu</given-names></name>
<xref ref-type="aff" rid="aff5"><sup>5</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Software" vocab-term-identifier="https://credit.niso.org/contributor-roles/software/">Software</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &amp; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-review-editing/">Writing &#x2013; review &#x00026; editing</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Validation" vocab-term-identifier="https://credit.niso.org/contributor-roles/validation/">Validation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Formal analysis" vocab-term-identifier="https://credit.niso.org/contributor-roles/formal-analysis/">Formal analysis</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<uri xlink:href="https://loop.frontiersin.org/people/1620642"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Zhang</surname> <given-names>Shuping</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Resources" vocab-term-identifier="https://credit.niso.org/contributor-roles/resources/">Resources</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Project administration" vocab-term-identifier="https://credit.niso.org/contributor-roles/project-administration/">Project administration</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &amp; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-review-editing/">Writing &#x2013; review &#x00026; editing</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Validation" vocab-term-identifier="https://credit.niso.org/contributor-roles/validation/">Validation</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing &#x2013; original draft</role>
<uri xlink:href="https://loop.frontiersin.org/people/460471"/>
</contrib>
</contrib-group>
<aff id="aff1"><label>1</label><institution>Department of Pathobiology and Integrative Biomedical Sciences, College of Veterinary Medicine, University of Missouri</institution>, <city>Columbia, MO</city>, <country country="us">United States</country></aff>
<aff id="aff2"><label>2</label><institution>Department of Public Health, College of Health Sciences, University of Missouri</institution>, <city>Columbia, MO</city>, <country country="us">United States</country></aff>
<aff id="aff3"><label>3</label><institution>MU Institute of Data Science and Informatics, University of Missouri</institution>, <city>Columbia, MO</city>, <country country="us">United States</country></aff>
<aff id="aff4"><label>4</label><institution>Veterinary Medical Diagnostic Laboratory, College of Veterinary Medicine, University of Missouri</institution>, <city>Columbia, MO</city>, <country country="us">United States</country></aff>
<aff id="aff5"><label>5</label><institution>Department of Natural Resources, Faculty of Geo-Information Science and Earth Observation, University of Twente</institution>, <city>Enschede</city>, <country>Netherlands</country></aff>
<author-notes>
<corresp id="c001"><label>&#x0002A;</label>Correspondence: Ram K. Raghavan, <email xlink:href="mailto:raghavanrk@missouri.edu">raghavanrk@missouri.edu</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-01-23">
<day>23</day>
<month>01</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>12</volume>
<elocation-id>1658248</elocation-id>
<history>
<date date-type="received">
<day>02</day>
<month>07</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>03</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>15</day>
<month>12</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2026 Raghavan, Ierardi, Osei and Zhang.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Raghavan, Ierardi, Osei and Zhang</copyright-holder>
<license>
<ali:license_ref start_date="2026-01-23">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>Bovine anaplasmosis, caused by the rickettsia <italic>Anaplasma marginale</italic>, is an economically important and globally distributed tick- and blood-borne disease of cattle. Although cases are known to be widespread in Missouri, current spatiotemporal trends, presence of high-risk areas, and any potential drivers for disease trends in Missouri are poorly documented. To address these knowledge gaps, this study analyzed spatiotemporal patterns of annual, county-level anaplasmosis case counts using a Bayesian hierarchical framework. Seropositive cases of anaplasmosis detected at the University of Missouri Veterinary Medical Diagnostic Laboratory (<italic>n</italic> = 1,944) between the years 2010&#x02013;2021 were used to construct data-driven Bayesian hierarchical models. All the models consisted of imputation sub-models to alleviate issues related to missing observations from spatiotemporal units (114 counties and 1 independent city, 12 years). Three progressively complex models with different assumptions for capturing the spatial, temporal, and spatiotemporal interactions that explained the variability in case counts were prepared. Model-1 included linear predictors decomposed into structured and unstructured terms for the temporal and spatial processes. Model-2 included separate temporal terms for smoothing each spatial entity and spatial smoothing terms for each temporal entity. This model was extended in Model-3, which included space-time interaction effect using first-order conditional autoregressive (CAR) priors. Based on the Deviance Information Criterion (DIC), Model 3 was superior at explaining space/time variability in the detected seropositive cases of bovine anaplasmosis. These findings indicate that distribution and risk of bovine anaplasmosis seroprevalence in Missouri are non-uniform, and potentially driven by environmental and/or management factors, operating at local and regional scales, that when identified could inform mitigation strategies.</p></abstract>
<kwd-group>
<kwd><italic>Anaplasma marginale</italic></kwd>
<kwd>Bayesian spatiotemporal analysis</kwd>
<kwd>bovine anaplasmosis</kwd>
<kwd>imputation model</kwd>
<kwd>missingness</kwd>
</kwd-group>
<funding-group>
 <funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This project partially was supported by Taylor Geospatial Institute GISCoR (Geospatial Institute Seed Grant Program to stimulate Collaborative Research).</funding-statement>
</funding-group>
<counts>
<fig-count count="9"/>
<table-count count="2"/>
<equation-count count="6"/>
<ref-count count="52"/>
<page-count count="15"/>
<word-count count="7251"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Veterinary Epidemiology and Economics</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Bovine anaplasmosis, caused by the rickettsia <italic>Anaplasma marginale</italic>, is an economically important tick- and blood-borne disease of cattle found worldwide. Its clinical effects of severe anemia, weight loss, spontaneous abortions, and death negatively impact cattle welfare and create a significant economic burden for cattle producers (<xref ref-type="bibr" rid="B1">1</xref>). A vaccine that is consistently safe and effective has proved elusive (<xref ref-type="bibr" rid="B2">2</xref>). Treatment and control usually depends on administration of oral and/or injectable tetracyclines; however, this approach is not always effective (<xref ref-type="bibr" rid="B3">3</xref>) and may be associated with the development of antimicrobial resistance (<xref ref-type="bibr" rid="B4">4</xref>). Cattle that survive acute infection are lifelong subclinical carriers of <italic>A. marginale</italic> and represent a key reservoir of infection for other cattle through tick transmission, inadvertent mechanical transmission via blood-contaminated needles (<xref ref-type="bibr" rid="B5">5</xref>) and veterinary instruments, and mechanical transmission via certain biting flies (<xref ref-type="bibr" rid="B6">6</xref>, <xref ref-type="bibr" rid="B7">7</xref>).</p>
<p>Evidence suggests that bovine anaplasmosis is becoming more prevalent and more geographically widespread (<xref ref-type="bibr" rid="B8">8</xref>&#x02013;<xref ref-type="bibr" rid="B13">13</xref>). Spatiotemporal modeling demonstrated increases of anaplasmosis in Kansas since 2005 (<xref ref-type="bibr" rid="B14">14</xref>), where over 50% of beef herds are infected (<xref ref-type="bibr" rid="B15">15</xref>). Human tick-borne illnesses follow a similar trend, having increased significantly over the last decade (<xref ref-type="bibr" rid="B16">16</xref>), particularly in the midwestern U.S. Concurrently, expansion of the geographic distributions and active seasons of medically important ticks in North America has been well documented (<xref ref-type="bibr" rid="B17">17</xref>&#x02013;<xref ref-type="bibr" rid="B20">20</xref>), while human encroachment on tick habitats increases the likelihood of encounters (<xref ref-type="bibr" rid="B21">21</xref>).</p>
<p>In the U.S., bovine anaplasmosis is vectored by <italic>Dermacentor</italic> spp. including the American dog tick (<italic>D. variabilis</italic>), the Rocky Mountain wood tick (<italic>D. andersoni</italic>), the winter tick (<italic>D. albipictus</italic>), and the western dog tick, <italic>D</italic>. <italic>occidentalis</italic> (<xref ref-type="bibr" rid="B22">22</xref>). Both <italic>D. variabilis</italic> and <italic>D. albipictus</italic> are established in Missouri, although <italic>D. albipictus</italic> preferentially feeds on cervids (<xref ref-type="bibr" rid="B23">23</xref>). Distribution of tick-borne diseases, such as bovine anaplasmosis are often concordant with the spatial distribution of their transmitting vectors (<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B24">24</xref>, <xref ref-type="bibr" rid="B25">25</xref>), and are therefore indirectly affected by the natural fluctuations in climate and habitat availability for ticks and their hosts. In the case of bovine anaplasmosis, additional factors that may affect spatiotemporal distribution include management practices (<xref ref-type="bibr" rid="B5">5</xref>, <xref ref-type="bibr" rid="B26">26</xref>) and cattle movements leading to comingling of na&#x000EF;ve and carrier animals.</p>
<p>Spatiotemporal disease mapping models are a useful tool to describe such disease patterns, more specifically to identify the presence of any clusters of incidences over space, time, or both (<xref ref-type="bibr" rid="B27">27</xref>). The presence of such clusters often points to underlying management, environmental, or other factors that could be potentially driving the disease incidence, which can then be targeted for interventions, and resource allocation (<xref ref-type="bibr" rid="B28">28</xref>, <xref ref-type="bibr" rid="B29">29</xref>). Making inferences based on crude values of disease incidence over geographic space and time is problematic as the underlying spatiotemporal structure of the data is unaccounted for (<xref ref-type="bibr" rid="B27">27</xref>, <xref ref-type="bibr" rid="B30">30</xref>). Bayesian spatiotemporal models provide a robust and flexible platform for space-time analysis of disease incidences and have been utilized to explore the potential effects abiotic covariates such as climate and land cover features in the disease ecology. Such models have been applied to the study of bovine anaplasmosis and other tick-borne diseases (<xref ref-type="bibr" rid="B14">14</xref>, <xref ref-type="bibr" rid="B24">24</xref>, <xref ref-type="bibr" rid="B25">25</xref>).</p>
<p>The objective of this study was to evaluate the spatial, temporal, spatiotemporal risk patterns of bovine anaplasmosis in the Midwestern state of Missouri using a Bayesian approach with counts of bovine serum samples that tested positive via competitive ELISA (cELISA) at the University of Missouri Veterinary Medical Diagnostic Laboratory (MU VMDL) between the years 2010&#x02013;2021.</p></sec>
<sec sec-type="materials and methods" id="s2">
<label>2</label>
<title>Materials and methods</title>
<sec>
<label>2.1</label>
<title>Disease data</title>
<p>The VMDL&#x00027;s laboratory information management system, VetView (University of Georgia, Athens USA), was searched using the &#x0201C;Query Builder&#x0201D; tool for all accessions received January 1, 2010 through December 31, 2021 which included the test code for <italic>A. marginale</italic> competitive ELISA (cELISA). The resulting list of accessions was exported directly from VetView into Microsoft Excel as a .csv file, which included accession number, animal identification, and date of receipt. All case records were reviewed by a single observer (R. Ierardi) and the following items were manually entered into Microsoft Excel: owner&#x00027;s state, county, and city; veterinarian&#x00027;s state, county, and city; animal&#x00027;s age; animal&#x00027;s sex; and, the result of the <italic>A. marginale</italic> cELISA test (1 = positive, 0 = negative). The VMDL&#x00027;s cutoff for a positive result throughout the study period was &#x02265;30% inhibition, according to the manufacturer&#x00027;s instructions (<italic>Anaplasma</italic> Antibody Test Kit, cELISA v2; VMRD, Pullman, WA). The data was curated by excluding cases that met specific criteria (e.g., non-tested samples, samples of inappropriate type, etc.), submitted by owners out-of-state, and submitted by veterinarians out-of-state (<xref ref-type="table" rid="T1">Table 1</xref>).</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Year-specific and total records of bovine sera, regardless of cELISA result, exported from the VetView laboratory information management system (LIMS) at the University of Missouri Veterinary Medical Diagnostic Laboratory, 2010&#x02013;2021.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left"><bold>Year</bold></th>
<th valign="top" align="center"><bold>Version 1 (Raw)</bold></th>
<th valign="top" align="center"><bold>Non-tested</bold></th>
<th valign="top" align="center"><bold>Non-bovine</bold></th>
<th valign="top" align="center"><bold>Unsuitable</bold></th>
<th valign="top" align="center"><bold>Research</bold></th>
<th valign="top" align="center"><bold>Duplicate</bold></th>
<th valign="top" align="center"><bold>Version 2 (after criteria exclusions)</bold></th>
<th valign="top" align="center"><bold>Version 3 (after removing out-of-state owners)</bold></th>
<th valign="top" align="center"><bold>Version 4 (Final, after removing out-of-state veterinarians)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">2010</td>
<td valign="top" align="center">488</td>
<td valign="top" align="center">30</td>
<td valign="top" align="center">10</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">448</td>
<td valign="top" align="center">429</td>
<td valign="top" align="center">429</td>
</tr>
<tr>
<td valign="top" align="left">2011</td>
<td valign="top" align="center">519</td>
<td valign="top" align="center">10</td>
<td valign="top" align="center">3</td>
<td valign="top" align="center">1</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">505</td>
<td valign="top" align="center">355</td>
<td valign="top" align="center">310</td>
</tr>
<tr>
<td valign="top" align="left">2012</td>
<td valign="top" align="center">419</td>
<td valign="top" align="center">8</td>
<td valign="top" align="center">9</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">402</td>
<td valign="top" align="center">382</td>
<td valign="top" align="center">381</td>
</tr>
<tr>
<td valign="top" align="left">2013</td>
<td valign="top" align="center">290</td>
<td valign="top" align="center">4</td>
<td valign="top" align="center">5</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">281</td>
<td valign="top" align="center">261</td>
<td valign="top" align="center">256</td>
</tr>
<tr>
<td valign="top" align="left">2014</td>
<td valign="top" align="center">398</td>
<td valign="top" align="center">12</td>
<td valign="top" align="center">7</td>
<td valign="top" align="center">1</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">378</td>
<td valign="top" align="center">287</td>
<td valign="top" align="center">287</td>
</tr>
<tr>
<td valign="top" align="left">2015</td>
<td valign="top" align="center">459</td>
<td valign="top" align="center">6</td>
<td valign="top" align="center">16</td>
<td valign="top" align="center">2</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">435</td>
<td valign="top" align="center">381</td>
<td valign="top" align="center">381</td>
</tr>
<tr>
<td valign="top" align="left">2016</td>
<td valign="top" align="center">653</td>
<td valign="top" align="center">24</td>
<td valign="top" align="center">15</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">4</td>
<td valign="top" align="center">610</td>
<td valign="top" align="center">533</td>
<td valign="top" align="center">530</td>
</tr>
<tr>
<td valign="top" align="left">2017</td>
<td valign="top" align="center">588</td>
<td valign="top" align="center">7</td>
<td valign="top" align="center">2</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">2</td>
<td valign="top" align="center">577</td>
<td valign="top" align="center">496</td>
<td valign="top" align="center">496</td>
</tr>
<tr>
<td valign="top" align="left">2018</td>
<td valign="top" align="center">520</td>
<td valign="top" align="center">14</td>
<td valign="top" align="center">1</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">505</td>
<td valign="top" align="center">330</td>
<td valign="top" align="center">330</td>
</tr>
<tr>
<td valign="top" align="left">2019</td>
<td valign="top" align="center">567</td>
<td valign="top" align="center">14</td>
<td valign="top" align="center">4</td>
<td valign="top" align="center">4</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">545</td>
<td valign="top" align="center">319</td>
<td valign="top" align="center">319</td>
</tr>
<tr>
<td valign="top" align="left">2020</td>
<td valign="top" align="center">631</td>
<td valign="top" align="center">65</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">7</td>
<td valign="top" align="center">2</td>
<td valign="top" align="center">557</td>
<td valign="top" align="center">290</td>
<td valign="top" align="center">289</td>
</tr>
<tr>
<td valign="top" align="left">2021</td>
<td valign="top" align="center">537</td>
<td valign="top" align="center">8</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">0</td>
<td valign="top" align="center">529</td>
<td valign="top" align="center">309</td>
<td valign="top" align="center">308</td>
</tr>
<tr>
<td valign="top" align="left">Total</td>
<td valign="top" align="center">6,069</td>
<td valign="top" align="center">202</td>
<td valign="top" align="center">72</td>
<td valign="top" align="center">8</td>
<td valign="top" align="center">7</td>
<td valign="top" align="center">8</td>
<td valign="top" align="center">5,772</td>
<td valign="top" align="center">4,372</td>
<td valign="top" align="center">4,316</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Version 1 = raw data exports; Version 2 = after removing records meeting specific criteria (non-tested, non-bovine, unsuitable sample, research, duplicates); Version 3 = after removing out-of-state owners; Version 4 = after removing out-of-state veterinarians (final dataset). Exclusions between Versions 1 and 2 are detailed by category.</p>
</table-wrap-foot>
</table-wrap>
<p>For each of the 12 years, VetView was queried for samples received January 1 through December 31. A species filter was not applied at the time of the original queries for 2010&#x02013;2019, and non-bovine samples were removed after data entry was completed. A &#x0201C;Bovine&#x0201D; species filter was applied at the time of the original queries for 2020&#x02013;2021. For each year, VetView would export a list of accessions as a .csv file, each having a column with the date of receipt and another column with a list of comma-separated sample IDs for each accession. Note that VetView&#x00027;s list of samples for a given accession may include multiple sample types destined for different tests. The sample ID column was split by comma delimiter to rows, thus yielding the total number of individual samples received for each year.</p></sec>
<sec>
<label>2.2</label>
<title>Data curation</title>
<p>The queried data Version 1 for 2010&#x02013;2021 contained 6,069 records, which were subsequently reduced to a subset (Version 2) following the removal of sample IDs that were not tested for anaplasmosis, sample IDs that were not from cattle (usually from other ruminants), and other criteria (<xref ref-type="table" rid="T1">Table 1</xref>). This resulted in the removal of 297 records. Version 2 (5,772 records) was further filtered to retain only records in which the owner&#x00027;s state was listed as Missouri, or the owner&#x00027;s state was not specified, and the veterinarian&#x00027;s state was Missouri, i.e., if the owner&#x00027;s state was not specified and the veterinarian&#x00027;s state was not Missouri, those records were removed. This resulted in the removal of 1,400 out-of-state records for a new total of 4,372 records (Version 3). Finally, observations where the owner&#x00027;s state was listed as Missouri but the veterinarian was from another state (56 records) were removed; in all of these cases, the owner&#x00027;s residence was in a county adjacent to the state line and often in a metropolitan area&#x02014;particularly St. Louis&#x02014;and therefore it was doubtful whether the owner&#x00027;s address was a reasonable proxy for the location of the cattle herd. This resulted in a final total of 4,316 records (Version 4) for analysis.</p></sec>
<sec>
<label>2.3</label>
<title>Geographic data</title>
<p>A 2010 TIGER/Line<sup>&#x000AE;</sup> shapefile for Missouri counties was downloaded from U.S. Census Bureau (<ext-link ext-link-type="uri" xlink:href="https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html">https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html</ext-link>). The shapefile included two polygons labeled &#x0201C;St. Louis&#x0201D;; St. Louis County and the independent city of St. Louis, which needed to be distinguished as separate polygons for our analysis. Therefore in RStudio, unique numeric identifiers were assigned to a list of Missouri&#x00027;s alphabetically sorted counties. These numeric county IDs were then appended to the shapefile&#x00027;s attribute table, carefully verifying the county names, and subsequently used as the join field to link with the anaplasmosis dataset using the &#x0201C;Add Join&#x0201D; tool.</p></sec>
<sec>
<label>2.4</label>
<title>Statistical modeling</title>
<p>A binomial hierarchical mixture model was considered for two reasons. Firstly, the disaggregation of the observed data into a space-time framework leads to many missing data points for both the observed outcomes and the expected seropositivity to bovine anaplasmosis in the population. Secondly, this approach seeks to accommodate imperfect detection of anaplasmosis in the population. Hence, the anaplasmosis counts in the present study are modeled as Binomial random variables. This class of models has proved useful in species population distribution models for estimating uncertainties in local abundance and detection probability (<xref ref-type="bibr" rid="B31">31</xref>&#x02013;<xref ref-type="bibr" rid="B33">33</xref>). A joint Bayesian analysis and imputation model was developed with a joint density described as</p>
<disp-formula id="E1"><mml:math id="M1"><mml:mtable columnalign="right"><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mi>&#x003B2;</mml:mi><mml:mtext>&#x000A0;</mml:mtext><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>&#x003B1;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>|</mml:mo><mml:mi>&#x003B2;</mml:mi><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x000D7;</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>&#x003B1;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where the Binomial (positive) outcomes <italic>y</italic><sub><italic>i</italic></sub> from the samples <inline-formula><mml:math id="M2"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> have known <inline-formula><mml:math id="M3"><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math></inline-formula> and missing <inline-formula><mml:math id="M4"><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> sample sizes. The Bayesian <italic>analysis model</italic> is therefore expressed as:</p>
<disp-formula id="E2"><mml:math id="M5"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x0007E;</mml:mo><mml:mi>B</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003C0;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>&#x003C0;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="script">S</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo class="qopname">exp</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x0002B;</mml:mo><mml:mo class="qopname">exp</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>&#x003B3;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B4;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where the <italic>i</italic> &#x0003D; 1, &#x02026;, <italic>N</italic> observations are disaggregated by <italic>j</italic> &#x0003D; 1, &#x02026;, <italic>J</italic> time steps (years) and <italic>k</italic> &#x0003D; 1, &#x02026;, <italic>K</italic> spatial locations, in this case, individual counties in Missouri. We project the infection probability &#x003C0;<sub><italic>i</italic></sub>on the linear predictor using the logistic sigmoid function <inline-formula><mml:math id="M6"><mml:mrow><mml:mi mathvariant="script">S</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> to ensure an output range between 0 and 1. The coefficient, if exponentiated exp(&#x003B2;<sub>0</sub>), represents the overall odds of anaplasmosis infection. The mixture probabilities (<italic>p</italic><sub>&#x003B3;[<italic>j</italic>]</sub> and <italic>p</italic><sub><italic>u</italic>[<italic>k</italic>]</sub>) are to prevent temporal (structured &#x003B3;<sub><italic>i</italic>[<italic>j</italic>]</sub> and unstructured &#x003B4;<sub><italic>i</italic>[<italic>j</italic>]</sub>) and spatial (structured <italic>u</italic><sub><italic>i</italic>[<italic>k</italic>]</sub> and unstructured <italic>v</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>) over-smoothing over large discontinuities, respectively.</p>
<p>The sample size <inline-formula><mml:math id="M7"><mml:msub><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:math></inline-formula> is a combination of observed samples <inline-formula><mml:math id="M8"><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup></mml:math></inline-formula> and missing samples <inline-formula><mml:math id="M9"><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula>. Since no information is available about the missingness of the observations, they were assumed to be missing at random (MAR), and a Bayesian imputation model was imposed for their prediction. The next stage of the model was the <italic>imputation model</italic>, which is to impute the missing samples as Poisson random variables with the total cattle counts <italic>m</italic><sub><italic>i</italic></sub> as offset, structured as</p>
<disp-formula id="E3"><mml:math id="M10"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mi>&#x003B1;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x0007E;</mml:mo><mml:mi>P</mml:mi><mml:mi>o</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>&#x003BB;</mml:mtext></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo class="qopname">log</mml:mo><mml:msub><mml:mrow><mml:mtext>&#x003BB;</mml:mtext></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0007E;</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B1;</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mtext>&#x003BB;</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Here, we use the average spatial process <italic>z</italic><sub><italic>i</italic>[<italic>k</italic>]</sub> of all the temporal steps centered by the intercept term &#x003B1;<sub>0</sub> to borrow strength between neighboring observations.</p>
<p>In the Bayesian context, the next stage in modeling is the functional forms of the process layers, &#x003B3;<sub><italic>i</italic>[<italic>j</italic>]</sub>, &#x003B4;<sub><italic>i</italic>[<italic>j</italic>]</sub>, <italic>v</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>, <italic>u</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>, <italic>U</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>. Based on different functional forms for the space, time, and space-time variables, three models were built. Model-1 includes a linear predictor that is decomposed into global spatial and temporal variations; that is</p>
<disp-formula id="E4"><mml:math id="M11"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>&#x003B3;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B4;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where, &#x003B3;<sub><italic>i</italic>[<italic>j</italic>]</sub> and &#x003B4;<sub><italic>i</italic>[<italic>j</italic>]</sub> are structured and unstructured temporal trends; and <italic>u</italic><sub><italic>i</italic>[<italic>k</italic>]</sub> and <italic>v</italic><sub><italic>i</italic>[<italic>k</italic>]</sub> are structured and unstructured spatial trends. For the structured temporal trends, a first-order random walk process was imposed such that &#x003B3;<sub><italic>i</italic>[<italic>j</italic>]</sub>&#x0007E;<italic>N</italic>(&#x003B3;<sub><italic>i</italic>[<italic>j</italic>&#x02212;1]</sub>, &#x003C4;<sub>&#x003B3;</sub>) for <italic>j</italic> &#x0003D; 2, &#x02026;, <italic>J</italic> and &#x003B3;<sub><italic>i</italic>[1]</sub>&#x0007E;<italic>N</italic>(0, &#x003C4;<sub>&#x003B3;</sub>). Here, the &#x003B4;<sub><italic>i</italic>[<italic>j</italic>]</sub> and <italic>v</italic><sub><italic>i</italic>[<italic>k</italic>]</sub> were modeled as exchangeable random intercepts, where &#x003B4;<sub><italic>i</italic>[<italic>j</italic>]</sub>&#x0007E;<italic>N</italic>(0, &#x003C4;<sub>&#x003B3;</sub>), <italic>v</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>&#x0007E;<italic>N</italic>(0, &#x003C4;<sub><italic>v</italic></sub>), for global temporal and spatial smoothing, respectively. For the structured spatial random effects <italic>u</italic><sub><italic>i</italic>[<italic>k</italic>]</sub>, a Gaussian Markov random field (GMRF) process was chosen for local smoothing. The precision matrix for the GMRF smoothing was based upon the spatial arrangements of the Missouri counties. The precision matrix has entries of &#x02212;1 for counties that are neighbors, 0 for those that are not neighbors, and the number of neighboring counties as the diagonal elements. To reduce over-smoothing over large discontinuities, the random effects, temporal, and spatial terms were modeled as mixture random effects with mixture probabilities <italic>p</italic><sub>&#x003B3;[<italic>j</italic>]</sub> and <italic>p</italic><sub><italic>u</italic>[<italic>k</italic>]</sub>, respectively.</p>
<p>In Model-2, a separate temporal smoothing function was introduced for each spatial entity, and a separate spatial smoothing function was introduced for each temporal unit; thus,</p>
<disp-formula id="E5"><mml:math id="M12"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>&#x003B7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>&#x003B3;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>&#x003B3;</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>&#x003B4;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>&#x0002B;</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Model-2 assumes no space-time interaction effects but relaxes the assumption of universal spatial smoothing across all time points and temporal smoothing across all spatial entities.</p>
<p>Model-3 is an extension of Model-2 with additional space-time interaction effects. Here, a first-order dynamic CAR was specified, where <italic>j</italic> &#x0003D; 2, &#x02026;, <italic>J</italic>, and <italic>u</italic><sub><italic>i</italic>[<italic>j, k</italic>]</sub> &#x0003D; &#x003C1;<sub><italic>i</italic>[<italic>k</italic>]</sub><italic>u</italic><sub><italic>i</italic>[<italic>j</italic>&#x02212;1, <italic>k</italic>]</sub>&#x0002B;<italic>w</italic><sub><italic>i</italic>[<italic>j, k</italic>]</sub>, where <italic>u</italic><sub><italic>i</italic>[1, <italic>k</italic>]</sub> is an average CAR spatial process and <italic>w</italic><sub><italic>i</italic>[<italic>j, k</italic>]</sub> are time-specific CAR processes. This is motivated by the class of dynamic models proposed by Gelfand, et al. (<xref ref-type="bibr" rid="B34">34</xref>). The temporal smoothing parameter &#x003C1;<sub><italic>i</italic>[<italic>k</italic>]</sub> spatially varies across the <italic>k</italic> spatial components. The mixture probabilities <italic>p</italic><sub>&#x003B3;[<italic>j, k</italic>]</sub> and <italic>p</italic><sub><italic>u</italic>[<italic>j, k</italic>]</sub> were modeled as random probabilities sampled from the Beta distribution; <italic>p</italic><sub>&#x003B3;[<italic>j, k</italic>]</sub>&#x0007E;&#x003B2;(1, 1), <italic>p</italic><sub><italic>u</italic>[<italic>j, k</italic>]</sub>&#x0007E;&#x003B2;(1, 1). Similarly, the common smoothing parameter was modeled as &#x003C1;<sub><italic>i</italic>[<italic>k</italic>]</sub>&#x0007E;&#x003B2;(1, 1 ).</p>
<p>Finally, hyper-parameters were assigned to all the variance components, <inline-formula><mml:math id="M13"><mml:msubsup><mml:mrow><mml:mi>&#x003C3;</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula>. For <inline-formula><mml:math id="M14"><mml:msubsup><mml:mrow><mml:mi>&#x003C3;</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x003C4;</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mo>&#x02022;</mml:mo></mml:mrow><mml:mo>}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula>, &#x003C4;<sub>{&#x02022;}</sub>&#x0007E;&#x003B3;(0.5, 0.05) was assigned. The model was simulated using the <italic>R2jags</italic> R package (<xref ref-type="bibr" rid="B35">35</xref>) with two chains for 10,000 iterations each. The first 5,000 iterations were discarded, and the remaining 5,000 iterations for each chain were used for making Bayesian inference. Autocorrelation trace plots of the MCMC samples were checked for convergence, and the discrepancy function below was used as the goodness-of-fit statistic to check the adequacy of the models by comparing the observed and predicted anaplasmosis counts.</p>
<disp-formula id="E6"><mml:math id="M15"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>&#x003C7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">{</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:mtext>&#x01D53C;</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mo>&#x02026;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo stretchy="false">}</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>V</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>|</mml:mo><mml:mo>&#x02026;</mml:mo></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>This statistic is computed for the observed and predicted anaplasmosis counts and then compared for each MCMC iteration. The binomial expectation for the observed <italic>E</italic>(<italic>y</italic><sub><italic>i</italic></sub>|&#x02026;) &#x0003D; <italic>n</italic><sub><italic>i</italic></sub><italic>p</italic><sub><italic>i</italic></sub> matches that of the predicted. Similarly, the binomial variance of the observed anaplasmosis counts, <italic>V</italic>(<italic>y</italic><sub><italic>i</italic></sub>|&#x02026;) &#x0003D; (1&#x02212;<italic>p</italic>)<italic>E</italic>(<italic>y</italic><sub><italic>i</italic></sub>|&#x02026;), equals that of the predicted counts. These two values are compared by calculating the Bayesian exceedance probabilities <inline-formula><mml:math id="M16"><mml:mo class="qopname">Pr</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mi>&#x003C7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>o</mml:mi><mml:mi>b</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:munderover><mml:mo>&#x02265;</mml:mo><mml:msubsup><mml:mrow><mml:mi>&#x003C7;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:math></inline-formula>. If there is no significant difference between the observed and predicted counts, the Bayesian <italic>p</italic>-values should be approximately 0.5. Bayesian <italic>p</italic>-values of &#x0003C; 0.1 or &#x0003E;0.9 are considered extreme (<xref ref-type="bibr" rid="B36">36</xref>).</p>
<p>A simpler explanation of the main differences between models 1, 2, and 3 and the reason for including a space-time interaction effect is provided in <xref ref-type="supplementary-material" rid="SM1">Supplementary File 1</xref>.</p></sec></sec>
<sec sec-type="results" id="s3">
<label>3</label>
<title>Results</title>
<sec>
<label>3.1</label>
<title>Descriptive statistics</title>
<p>The final dataset used for analysis in this study (4,316 records) included 1,944 samples that tested positive for <italic>A. marginale</italic> by cELISA. The VMDL received a mean of 360 samples/year, with a mean of 162 positives/year (<xref ref-type="fig" rid="F1">Figure 1</xref>). The largest number of both total and positive samples was received in 2016 (total = 530, positives = 220), and the smallest in 2013 (total = 256, positives = 66). Over the 12-year study period, the VMDL received a mean of 37.5 samples/county, with a mean of 16.9 positives/county. As expected, no obvious trends were apparent when crude counts were plotted at the county level (<xref ref-type="fig" rid="F2">Figure 2</xref>).</p>
<fig position="float" id="F1">
<label>Figure 1</label>
<caption><p>Annual counts of bovine serum samples submitted for <italic>Anaplasma marginale</italic> cELISA at the University of Missouri Veterinary Medical Diagnostic Laboratory, 2010&#x02013;2021.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0001.tif">
<alt-text content-type="machine-generated">Bar chart showing the number of serum samples received from 2010 to 2021. Each year displays data in two categories: positive samples in red and total samples in blue. The total fluctuates, peaking in 2016, while positive samples remain relatively stable.</alt-text>
</graphic>
</fig>
<fig position="float" id="F2">
<label>Figure 2</label>
<caption><p>Raw proportions of bovine <italic>Anaplasma</italic> cELISA-positive records (normalized by all cELISA test records) submitted to the University of Missouri Veterinary Medical Diagnostic Laboratory, 2010&#x02013;2021, summarized by county.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0002.tif">
<alt-text content-type="machine-generated">Map of Missouri counties showing raw proportions of cELISA positive records from 2010 to 2021. Colors range from light yellow (less than or equal to 20%) to dark brown (100%). Some counties are striped, indicating no records. A scale bar and north arrow are included.</alt-text>
</graphic>
</fig></sec>
<sec>
<label>3.2</label>
<title>Model estimations</title>
<p>The dataset used for modeling contained approximately 58% missing records in the binomial sampling sizes, necessitating the inclusion of missing data imputation sub-models. These sub-models were identical across Models 1&#x02013;3. As illustrated in <xref ref-type="fig" rid="F3">Figure 3</xref>, the missing data imputation sub-model demonstrated strong predictive accuracy, with a coefficient of determination close to 1 (R<sup>2</sup> &#x02248; 1). This imputation approach allowed for the use of the full dataset without excluding missing records.</p>
<fig position="float" id="F3">
<label>Figure 3</label>
<caption><p>Predictive accuracy of the missing data imputation sub-model. Strong predictive accuracy is visible, with a coefficient of determination close to 1.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0003.tif">
<alt-text content-type="machine-generated">Scatter plot with observed counts on the y-axis and predicted counts on the x-axis. Points are orange circles, showing a positive correlation. A solid black line indicates perfect prediction, with two dashed gray lines illustrating potential deviations.</alt-text>
</graphic>
</fig>
<p><xref ref-type="table" rid="T2">Table 2</xref> presents the DIC values used for model comparison. A lower DIC value indicates a better model. Model-3 outperforms the baseline Model-1 as well as Model-2. This outcome is anticipated since Model-1 applies global temporal and spatial smoothing functions, which is overly simplistic and impractical, particularly when the data is unstructured. Model-2 shares structural similarities with Model-3, as it applies separate spatial (temporal) smoothing to each temporal (spatial) unit. However, Model-3 surpasses Model-2 due to the inclusion of space-time interaction effects, which are essential for capturing the spatiotemporal dynamics of biological processes influencing anaplasmosis epidemiology. Consequently, all subsequent adequacy checks and interpretations were based on Model-3 alone.</p>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Evaluation parameters of the three Bayesian models constructed in the study.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left"><bold>Model</bold></th>
<th valign="top" align="center"><bold>Deviance information criterion</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Model-1</td>
<td valign="top" align="center">7,606.694</td>
</tr>
<tr>
<td valign="top" align="left">Model-2</td>
<td valign="top" align="center">5,223.553</td>
</tr>
<tr>
<td valign="top" align="left">Model-3</td>
<td valign="top" align="center">5,171.446</td>
</tr></tbody>
</table>
<table-wrap-foot>
<p>Lower Deviance Information Criterion (DIC) values indicate better model performance.</p>
</table-wrap-foot>
</table-wrap>
<p>Model-3 includes a single fixed effect, &#x003B2;<sub>0</sub> = &#x02212;0.4, with a logit-inverse value of <italic>logit inverse</italic>(&#x003B2;<sub>0</sub>) = 0.40. This value represents the average risk of anaplasmosis infection, accounting for unknown exposure effects captured through space-time interaction effects.</p>
<p>Plots of risk for the individual random effect components, derived from the logit inverse of posterior Bayesian estimates in Model-3, revealed a non-uniform spatiotemporal distribution of bovine anaplasmosis seroprevalence risk across Missouri counties. The overall spatial trend, assessed through the spatially structured and unstructured random effect components of Model-3, is presented in <xref ref-type="fig" rid="F4">Figures 4</xref>, <xref ref-type="fig" rid="F5">5</xref>. Likewise, the overall temporal trend, evaluated using the temporally structured and unstructured random effects, is shown in <xref ref-type="fig" rid="F6">Figure 6</xref>. Finally, the spatiotemporal risk is depicted through the structured spatiotemporal random effect (<xref ref-type="fig" rid="F7">Figure 7</xref>) and the spatiotemporally unstructured random effect term (<xref ref-type="fig" rid="F8">Figure 8</xref>).</p>
<fig position="float" id="F4">
<label>Figure 4</label>
<caption><p>County-specific Bayesian posterior risk estimates of overall structured spatial heterogeneity.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0004.tif">
<alt-text content-type="machine-generated">Map of Missouri showing spatial heterogeneity risk by county. Yellow indicates low risk, orange medium risk, and dark red high risk. Counties in the central and southeastern areas mostly show high risk.</alt-text>
</graphic>
</fig>
<fig position="float" id="F5">
<label>Figure 5</label>
<caption><p>County-specific Bayesian posterior risk estimates of overall unstructured spatial heterogeneity.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0005.tif">
<alt-text content-type="machine-generated">Map of Missouri showing overall uncorrelated spatial heterogeneity risk by county. Counties are shaded in three colors: light tan for low risk (less than 0.5), medium brown for medium risk (0.5 to 0.6), and dark brown for high risk (greater than 0.6). A scale and north arrow are included.</alt-text>
</graphic>
</fig>
<fig position="float" id="F6">
<label>Figure 6</label>
<caption><p>Purely temporal trends in Bayesian posterior mean risk along with 2.5% and 97.5% credible interval bounds of bovine anaplasmosis seropositivity risk in Missouri, 2010&#x02013;2021, evaluated with structured <bold>(top)</bold> and unstructured <bold>(bottom)</bold> random effects.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0006.tif">
<alt-text content-type="machine-generated">Twelve maps show changes in data across Missouri counties from 2010 to 2021. Each map is labeled with a year and features varying shades, representing different data levels. Darker shades seem concentrated in the northwest and southeast regions of the state over the years.</alt-text>
</graphic>
</fig>
<fig position="float" id="F7">
<label>Figure 7</label>
<caption><p>County- and year-specific Bayesian posterior risk estimates of structured spatial heterogeneity. Contiguous counties with similar colors indicate presence of same or similar underlying spatial processes that affect bovine anaplasmosis seroprevalence. Varying trends of higher and lower disease risk appearing to expand and contract over the years is observed.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0007.tif">
<alt-text content-type="machine-generated">A grid of maps depicting Missouri from 2010 to 2021, each showing county-level data with varying shades of brown and beige. The maps illustrate changes across years, possibly representing demographic or statistical information.</alt-text>
</graphic>
</fig>
<fig position="float" id="F8">
<label>Figure 8</label>
<caption><p>County- and year-specific Bayesian posterior risk estimates of spatially unstructured heterogeneity. Darker colors indicate anaplasmosis prevalence in those counties is driven by unique factors, rather than broader spatial processes operating at larger geographic scales spanning multiple contiguous counties. No trend is observed.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0008.tif">
<alt-text content-type="machine-generated">Two line graphs depicting temporal heterogeneity from 2008 to 2022. The top graph shows overall structured heterogeneity with a red line for the posterior mean, and dotted lines for the 2.5% and 97.5% credible bounds. The bottom graph shows overall unstructured heterogeneity with a green line for the posterior mean, and dotted lines for the 2.5% and 97.5% credible bounds. Trends indicate variations in risk over time.</alt-text>
</graphic>
</fig>
<p>Spatiotemporal plots of Bayesian <italic>p</italic>-values for exceedance probability (<xref ref-type="fig" rid="F9">Figure 9</xref>) indicate that while Model-3 performs well for most counties in Missouri, there is a consistent set of counties where the model underperforms.</p>
<fig position="float" id="F9">
<label>Figure 9</label>
<caption><p>Bayesian <italic>P-</italic>values of exceedance probabilities comparing county- and year-specific observed and predicted bovine anaplasmosis seropositivity counts. Counties with extreme <italic>p</italic>-values &#x0003C; 0.1 and &#x0003E;0.9, indicating poor predictive performance, are highlighted in dark gray. For most years, the model performance is poor in a consistent set of Missouri counties.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fvets-12-1658248-g0009.tif">
<alt-text content-type="machine-generated">Twelve maps of Missouri from 2010 to 2021 show counties highlighted in gray, indicating changes over the years. The maps are arranged in a grid, with each row representing a different year from 2010 to 2021.</alt-text>
</graphic>
</fig>
</sec></sec>
<sec sec-type="discussion" id="s4">
<label>4</label>
<title>Discussion</title>
<p>Bovine anaplasmosis is endemic in Missouri, with an estimated statewide seroprevalence of 46.5%. (<xref ref-type="bibr" rid="B37">37</xref>). This study analyzed the current spatial and spatiotemporal patterns in the disease&#x00027;s distribution across the state using retrospective diagnostic data routinely recorded in a laboratory information management system (LIMS), often a source of information for making epidemiological and disease management decisions (<xref ref-type="bibr" rid="B38">38</xref>, <xref ref-type="bibr" rid="B39">39</xref>). The Bayesian models considered in this study were data-driven, and the better performing model (Model-3) utilizes the CAR autocorrelation, which is effective in borrowing information from neighboring space-time units (<xref ref-type="bibr" rid="B27">27</xref>, <xref ref-type="bibr" rid="B40">40</xref>&#x02013;<xref ref-type="bibr" rid="B42">42</xref>). A strength of the models in this study is their ability to accommodate missing counts as well as missing sampling sizes, which alleviates the missing data problem often encountered in passive surveillance datasets. Such model structure is widely applied in site-occupancy models for accommodating local population uncertainties (<xref ref-type="bibr" rid="B33">33</xref>), and could be useful in situations similar to ours wherein LIMS data are assessed. The risk calculated in this study, i.e., the inverse logit of Bayesian posterior means for the purely spatial, purely temporal, and spatiotemporal random effects fitted in Model-3 reveal the spatial, temporal, and spatiotemporal trends for bovine anaplasmosis seropositivity over the 12-year study period.</p>
<p>The overall structured spatial heterogeneity (<xref ref-type="fig" rid="F4">Figure 4</xref>), when classified in three categories (low, medium, and high risk), shows clusters of high-risk counties for bovine anaplasmosis seropositivity along the eastern half of the state, in the north, central and southeast, while the medium and low risk counties are found throughout, and are also found in contiguous groups of counties. This suggests that the underlying spatial processes that drive such clustering are likely to be similar or potentially arise from the same source, i.e., environmental, disease management practices by producers and veterinarians, or other similar factors. The overall unstructured spatial heterogeneity on the other hand (<xref ref-type="fig" rid="F5">Figure 5</xref>) does not reveal any clustering, suggesting that there is no consistency in the effect of any local (or county-level) factors that play a major role in the spatial dynamics of bovine anaplasmosis seroprevalence in Missouri. The temporally structured and unstructured heterogeneity that accounted for the temporal effect in the retrospective dataset are presented in <xref ref-type="fig" rid="F6">Figure 6</xref>, revealing that the risk of observing bovine anaplasmosis seroprevalence in Missouri has changed over the study period, with some years recording higher risk than others. While the trend is non-linear, it appears the disease burden is more or less stable over the years in Missouri, with some noticeable interannual variability.</p>
<p>Choropleth plots showing posterior risk of structured spatiotemporal heterogeneity? (<xref ref-type="fig" rid="F7">Figure 7</xref>) indicates that the variations in presence of seropositive cases across Missouri counties are not independent but are spatially correlated, and shows a varying trend, with the disease risk appearing to expand and contract over the years. Disease risk increased significantly between 2010 and 2012, peaked around 2016, and again in 2019. The northeastern and southeastern regions consistently show higher risk throughout the years. After 2019, a decline in risk is noticeable; however, this trend could be likely due to less information available to the model that could be derived from the dataset for the latter years. Additionally, values outside these clusters change abruptly, with high and low-value counties scattered throughout the study area, sometimes in proximity. This pattern indicates that while the model successfully identifies regions potentially with similar characteristics affecting presence of seropositive cases, other unknown or unexamined factors may also contribute to the spatial distribution of the disease risk.</p>
<p>The risk maps of structured spatiotemporal heterogeneity further reveal that certain counties remain high-risk over multiple years, indicating persistent high-risk areas. These regions likely have stable environmental factors conducive to disease transmission, such as tick-favorable habitats or frequent livestock movement. Conversely, some counties consistently appear low-risk, representing stable low-risk areas where environmental or management conditions may naturally limit anaplasmosis transmission. Additionally, several counties exhibit fluctuating risk levels over time. Some areas increase in risk in later years, while others decline in risk. These shifts may result from interannual variations such as El Ni&#x000F1;o Southern Oscillation effects, seasonal variations, land use changes, or changes in disease management practices. Furthermore, emerging high-risk zones are evident, as some counties that were previously lower-risk become high-risk over time. This expansion of high-risk areas may be driven by factors such as climate change, shifts in livestock distribution, or increasing tick populations.</p>
<p>In contrast, the unstructured or spatially unstructured heterogeneity (<xref ref-type="fig" rid="F8">Figure 8</xref>) captures variations in anaplasmosis prevalence that are independent across counties, without spatial correlation to neighboring areas. Higher values suggest that anaplasmosis risk in those counties is driven by unique factors rather than broader spatial processes that operate at larger geographic scales spanning multiple contiguous counties. While values vary widely across the study area, no distinct clusters emerge. This indicates that although global trends exist, local deviations also occur, where specific local level factors may influence individual counties differently. Finally, the spatiotemporal plot of Bayesian <italic>p</italic>-values for exceedance probability (<xref ref-type="fig" rid="F9">Figure 9</xref>) indicates that while Model-3 performs well for a vast majority of the counties in Missouri, there is a consistent set of counties in Missouri where the model underperforms. One of the reasons for this underperformance could be related to fewer submissions from these counties to the VMDL, which are not adequately addressed by the missing data imputation method used. Additionally, this is also potentially due to the existence of unique factors that drive seropositivity risk in these counties, which are not adequately captured by the random effect terms included in Model-3. This can be alleviated by including biological (environmental, physical), and disease management-related variables that may capture the underlying spatiotemporal process more efficiently. Although our models did not directly evaluate the effects of environmental or management covariates, the spatial and temporal patterns observed in Missouri suggest that factors such as the distribution of wooded vs. open pastureland, regional variation in climate and vector habitat suitability, and differences in herd management practices (e.g., grazing intensity, herd movement, and vector control) may help explain variation in anaplasmosis risk. Incorporating these data into future analyses would allow for more precise assessments of how such factors shape disease dynamics and could guide the development of region-specific management strategies to reduce the burden of bovine anaplasmosis.</p></sec>
<sec id="s5">
<label>5</label>
<title>Conclusions</title>
<p>Clusters of high-risk counties scattered throughout the state (<xref ref-type="fig" rid="F4">Figure 4</xref>) suggest the presence of similar underlying processes that operate across local and/or regional scales and which are not captured in the present model. Possible explanatory variables include local variations in microhabitat and host abundance, which can influence populations of vector ticks, such as soil characteristics (<xref ref-type="bibr" rid="B43">43</xref>), encroachment by woody plants such as invasive red cedar (<xref ref-type="bibr" rid="B44">44</xref>), and variations in population density of white-tailed deer (<xref ref-type="bibr" rid="B45">45</xref>). Local differences in cattle population and movement are also likely to be involved. The lack of any statewide trend in plots of spatially unstructured heterogeneity (<xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F8">8</xref>) further illustrates the importance of local risk factors to anaplasmosis epidemiology in Missouri.</p>
<p>While the overall risk of bovine anaplasmosis seropositivity in Missouri appears relatively steady during the 12-year study period (<xref ref-type="fig" rid="F6">Figure 6</xref>), some fluctuation is nonetheless apparent. While some of this fluctuation may be attributable to random &#x0201C;noise&#x0201D; in the available data, other potential explanatory variables not captured in the present model include temporal fluctuations in weather patterns, which in turn can influence cattle population dynamics through their effects on market pressures. A specific example is the marked reduction in beef cow inventories prompted by drought in 2011&#x02013;2013, which reached its nadir in 2014 (<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>). This was eventually followed by restocking of herds, often with replacement heifers shipped in from out-of-state, which increases the opportunities for comingling of na&#x000EF;ve and carrier cattle (<xref ref-type="bibr" rid="B48">48</xref>). Temporal fluctuations in weather patterns are also likely to affect tick populations and host-seeking behaviors (<xref ref-type="bibr" rid="B49">49</xref>, <xref ref-type="bibr" rid="B50">50</xref>).</p>
<p>Plots of county- and year-specific spatially structured heterogeneity (<xref ref-type="fig" rid="F7">Figure 7</xref>) reveal four distinct situations: (1) counties that are consistently higher-risk, (2) counties that are consistently lower-risk, (3) counties that transition from lower to higher risk, and (4) counties that transition from higher to lower risk. Illustrated differently, if the faceted plot in <xref ref-type="fig" rid="F7">Figure 7</xref> were animated as a time series, the color gradient of certain counties would become progressively darker (increasing risk) or lighter (decreasing risk), sometimes multiple times during the study period. This is uncharacteristic of biological diffusion, i.e., &#x0201C;natural&#x0201D; spread of disease cases over space and time (<xref ref-type="bibr" rid="B51">51</xref>) and instead suggests introduction of cases via cattle movements, similar to the manner in which human diseases can appear in new locations via travel (<xref ref-type="bibr" rid="B52">52</xref>). Cattle movement, generally through markets, is strongly suspected to be an important source of variation in anaplasmosis risk around Missouri.</p>
<p>Finally, spatiotemporal plots of Bayesian <italic>p</italic>-values for exceedance probability (<xref ref-type="fig" rid="F9">Figure 9</xref>) indicate 13 counties where the model performs poorly. Some are likely attributable to insufficient submissions from these counties to the VMDL; the independent city of St. Louis, which, as expected for beef cattle, has no submissions during the study period, is perhaps the best example. Nonetheless, several other counties (such as Dunklin and New Madrid, in the &#x0201C;bootheel&#x0201D; of southeastern Missouri) are also without submissions during the study period and are not flagged as underperforming via exceedance probabilities. Further work is required to understand why Model-3 performs poorly in some counties. One potential way to improve the model performance is by including fixed effect terms that may have further explanatory potential, such as those in the categories of environmental, herd management, and tick distribution. The availability of such data at the scale of present analysis and their suitable spatial transformation may however be limited.</p></sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The data analyzed in this study is subject to the following licenses/restrictions: Data available for reasonable research use from the MU Veterinary Medical Diagnostic Laboratory. Requests to access these datasets should be directed to <email>raghavanrk&#x00040;missouri.edu</email>.</p>
</sec>
<sec sec-type="ethics-statement" id="s7">
<title>Ethics statement</title>
<p>Ethical approval was not required for the study involving animals in accordance with the local legislation and institutional requirements because This study used retrospective data that was anonymized prior to analysis.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>RR: Investigation, Validation, Visualization, Funding acquisition, Formal analysis, Data curation, Conceptualization, Resources, Project administration, Software, Writing &#x02013; review &#x00026; editing, Methodology, Supervision, Writing &#x02013; original draft. RI: Data curation, Visualization, Methodology, Investigation, Writing &#x02013; review &#x00026; editing, Writing &#x02013; original draft. FBO: Writing &#x02013; original draft, Software, Writing &#x02013; review &#x00026; editing, Validation, Formal analysis, Methodology, Conceptualization. SZ: Project administration, Writing &#x02013; review &#x00026; editing, Validation, Supervision, Writing &#x02013; original draft.</p>
</sec>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The author RR declared that they were an editorial board member of Frontiers at the time of submission. This had no impact on the peer review process and the final decision.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p></sec>
<sec sec-type="disclaimer" id="s11">
<title>Publisher&#x00027;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec sec-type="supplementary-material" id="s12">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fvets.2025.1658248/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fvets.2025.1658248/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="Table_1.docx" id="SM1" mimetype="application/vnd.openxmlformats-officedocument.wordprocessingml.document" xmlns:xlink="http://www.w3.org/1999/xlink"/></sec>
<ref-list>
<title>References</title>
<ref id="B1">
<label>1.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Railey</surname> <given-names>AF</given-names></name> <name><surname>Marsh</surname> <given-names>TL</given-names></name></person-group>. <article-title>Economic benefits of diagnostic testing in Livestock: anaplasmosis in cattle</article-title>. <source>Front Vet Sci</source>. (<year>2021</year>) <volume>8</volume>:<fpage>626420</fpage>. doi: <pub-id pub-id-type="doi">10.3389/fvets.2021.626420</pub-id><pub-id pub-id-type="pmid">34414221</pub-id></mixed-citation>
</ref>
<ref id="B2">
<label>2.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Salinas-Estrella</surname> <given-names>E</given-names></name> <name><surname>Amaro-Estrada</surname> <given-names>I</given-names></name> <name><surname>Cobaxin-C&#x000E1;rdenas</surname> <given-names>ME</given-names></name> <name><surname>Preciado de la Torre</surname> <given-names>JF</given-names></name> <name><surname>Rodr&#x000ED;guez</surname> <given-names>SD</given-names></name></person-group>. <article-title>Bovine Anaplasmosis: Will there ever be an almighty effective vaccine?</article-title> <source>Front Vet Sci.</source> (<year>2022</year>) <volume>9</volume>:<fpage>946545</fpage>. doi: <pub-id pub-id-type="doi">10.3389/fvets.2022.946545</pub-id><pub-id pub-id-type="pmid">36277070</pub-id></mixed-citation>
</ref>
<ref id="B3">
<label>3.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Curtis</surname> <given-names>AK</given-names></name> <name><surname>Kleinhenz</surname> <given-names>MD</given-names></name> <name><surname>Anantatat</surname> <given-names>T</given-names></name> <name><surname>Martin</surname> <given-names>MS</given-names></name> <name><surname>Magnin</surname> <given-names>GC</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <etal/></person-group>. <article-title>Failure to eliminate persistent <italic>Anaplasma marginale</italic> infection from cattle using labeled doses of chlortetracycline and oxytetracycline antimicrobials</article-title>. <source>Vet Sci.</source> (<year>2021</year>) <volume>20</volume>:<fpage>8</fpage>. doi: <pub-id pub-id-type="doi">10.3390/vetsci8110283</pub-id><pub-id pub-id-type="pmid">34822656</pub-id></mixed-citation>
</ref>
<ref id="B4">
<label>4.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Toillion</surname> <given-names>AR</given-names></name> <name><surname>Reppert</surname> <given-names>EJ</given-names></name> <name><surname>Amachawadi</surname> <given-names>RG</given-names></name> <name><surname>Olson</surname> <given-names>KC</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <name><surname>Kang</surname> <given-names>Q</given-names></name> <etal/></person-group>. <article-title>Effect of protracted free-choice chlortetracycline-medicated mineral for anaplasmosis control on Escherichia coli chlortetracycline resistance profile from pastured beef cattle</article-title>. <source>Microorganisms</source>. (<year>2021</year>) <volume>9</volume>:<fpage>2495</fpage>. doi: <pub-id pub-id-type="doi">10.3390/microorganisms9122495</pub-id><pub-id pub-id-type="pmid">34946097</pub-id></mixed-citation>
</ref>
<ref id="B5">
<label>5.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Reinbold</surname> <given-names>JB</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <name><surname>Hollis</surname> <given-names>LC</given-names></name> <name><surname>Nickell</surname> <given-names>JS</given-names></name> <name><surname>Riegel</surname> <given-names>CM</given-names></name> <name><surname>Christopher</surname> <given-names>JA</given-names></name> <etal/></person-group>. <article-title>Comparison of iatrogenic transmission of <italic>Anaplasma marginale</italic> in Holstein steers via needle and needle-free injection techniques</article-title>. <source>Am J Vet Res.</source> (<year>2010</year>) <volume>71</volume>:<fpage>1178</fpage>&#x02013;<lpage>88</lpage>. doi: <pub-id pub-id-type="doi">10.2460/ajvr.71.10.1178</pub-id><pub-id pub-id-type="pmid">20919904</pub-id></mixed-citation>
</ref>
<ref id="B6">
<label>6.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Scoles</surname> <given-names>GA</given-names></name> <name><surname>Miller</surname> <given-names>JA</given-names></name> <name><surname>Foil</surname> <given-names>LD</given-names></name></person-group>. <article-title>Comparison of the efficiency of biological transmission of <italic>Anaplasma marginale</italic> (Rickettsiales: Anaplasmataceae) by <italic>Dermacentor andersoni</italic> Stiles (Acari: Ixodidae) with mechanical transmission by the horse fly, <italic>Tabanus fuscicostatus</italic> Hine (Diptera: Muscidae)</article-title>. <source>J Med Entomol.</source> (<year>2008</year>) <volume>45</volume>:<fpage>109</fpage>&#x02013;<lpage>14</lpage>. doi: <pub-id pub-id-type="doi">10.1093/jmedent/45.1.109</pub-id><pub-id pub-id-type="pmid">18283950</pub-id></mixed-citation>
</ref>
<ref id="B7">
<label>7.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Scoles</surname> <given-names>GA</given-names></name> <name><surname>Broce</surname> <given-names>AB</given-names></name> <name><surname>Lysyk</surname> <given-names>TJ</given-names></name> <name><surname>Palmer</surname> <given-names>GH</given-names></name></person-group>. <article-title>Relative efficiency of biological transmission of <italic>Anaplasma marginale</italic> (Rickettsiales: Anaplasmataceae) by <italic>Dermacentor andersoni</italic> (Acari: Ixodidae) compared with mechanical transmission by <italic>Stomoxys calcitrans</italic> (Diptera: Muscidae)</article-title>. <source>J Med Entomol.</source> (<year>2005</year>) <volume>42</volume>:<fpage>668</fpage>&#x02013;<lpage>75</lpage>. doi: <pub-id pub-id-type="doi">10.1093/jmedent/42.4.668</pub-id><pub-id pub-id-type="pmid">16119558</pub-id></mixed-citation>
</ref>
<ref id="B8">
<label>8.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jones</surname> <given-names>AL</given-names></name> <name><surname>Berghaus</surname> <given-names>RD</given-names></name> <name><surname>Kalatari</surname> <given-names>AA</given-names></name> <name><surname>Credille</surname> <given-names>B</given-names></name> <name><surname>Naikare</surname> <given-names>HK</given-names></name> <name><surname>Heins</surname> <given-names>B</given-names></name> <etal/></person-group>. <article-title>Seroprevalence and molecular detection of <italic>Anaplasma marginale</italic> infected beef herds in Georgia, USA</article-title>. <source>Bovine Pract.</source> (<year>2022</year>) <volume>56</volume>:<fpage>70</fpage>&#x02013;<lpage>8</lpage>. doi: <pub-id pub-id-type="doi">10.21423/bovine-vol56no2p70-78</pub-id></mixed-citation>
</ref>
<ref id="B9">
<label>9.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Johnson-Walker</surname> <given-names>YJ</given-names></name> <name><surname>Steckler</surname> <given-names>T</given-names></name> <name><surname>Beever</surname> <given-names>J</given-names></name> <name><surname>Myint</surname> <given-names>MS</given-names></name> <name><surname>Rijwani</surname> <given-names>S</given-names></name> <name><surname>Beever</surname> <given-names>E</given-names></name></person-group>. <article-title>Epidemiology and economic impact of anaplasmosis in southern Illinois beef cattle</article-title>. <source>Int Symp Vet Epidemiol Econ</source>. (<year>2018</year>) <fpage>41</fpage>.</mixed-citation>
</ref>
<ref id="B10">
<label>10.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Okafor</surname> <given-names>CC</given-names></name> <name><surname>Collins</surname> <given-names>SL</given-names></name> <name><surname>Daniel</surname> <given-names>JA</given-names></name> <name><surname>Harvey</surname> <given-names>B</given-names></name> <name><surname>Sun</surname> <given-names>X</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <etal/></person-group>. <article-title>Factors associated with seroprevalence of anaplasma marginale in Kentucky cattle</article-title>. <source>Vet Parasitol Reg Stud Reports.</source> (<year>2018</year>) <volume>13</volume>:<fpage>212</fpage>&#x02013;<lpage>9</lpage>. doi: <pub-id pub-id-type="doi">10.1016/j.vprsr.2018.07.003</pub-id><pub-id pub-id-type="pmid">31014877</pub-id></mixed-citation>
</ref>
<ref id="B11">
<label>11.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Okafor</surname> <given-names>CC</given-names></name> <name><surname>Collins</surname> <given-names>SL</given-names></name> <name><surname>Daniel</surname> <given-names>JA</given-names></name> <name><surname>Harvey</surname> <given-names>B</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <name><surname>Whitlock</surname> <given-names>BK</given-names></name></person-group>. <article-title>Factors associated with seroprevalence of bovine anaplasmosis in Texas</article-title>. <source>Vet Parasitol Reg Stud Reports.</source> (<year>2018</year>) <volume>14</volume>:<fpage>32</fpage>&#x02013;<lpage>40</lpage>. doi: <pub-id pub-id-type="doi">10.1016/j.vprsr.2018.08.004</pub-id><pub-id pub-id-type="pmid">31014734</pub-id></mixed-citation>
</ref>
<ref id="B12">
<label>12.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Okafor</surname> <given-names>CC</given-names></name> <name><surname>Collins</surname> <given-names>SL</given-names></name> <name><surname>Daniel</surname> <given-names>JA</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <name><surname>Whitlock</surname> <given-names>BK</given-names></name></person-group>. <article-title>Seroprevalence of bovine anaplasmosis in Georgia</article-title>. <source>Vet Parasitol Reg Stud Reports.</source> (<year>2019</year>) <volume>15</volume>:<fpage>100258</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.vprsr.2018.100258</pub-id><pub-id pub-id-type="pmid">30929935</pub-id></mixed-citation>
</ref>
<ref id="B13">
<label>13.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Okafor</surname> <given-names>CC</given-names></name> <name><surname>Collins</surname> <given-names>SL</given-names></name> <name><surname>Daniel</surname> <given-names>JA</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name> <name><surname>Whitlock</surname> <given-names>BK</given-names></name></person-group>. <article-title>Factors associated with seroprevalence of bovine anaplasmosis in Mississippi, USA</article-title>. <source>Vet Parasitol Reg Stud Reports.</source> (<year>2019</year>) <volume>17</volume>:<fpage>100301</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.vprsr.2019.100301</pub-id><pub-id pub-id-type="pmid">31303216</pub-id></mixed-citation>
</ref>
<ref id="B14">
<label>14.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hanzlicek</surname> <given-names>GA</given-names></name> <name><surname>Raghavan</surname> <given-names>RK</given-names></name> <name><surname>Ganta</surname> <given-names>RR</given-names></name> <name><surname>Anderson</surname> <given-names>GA</given-names></name></person-group>. <article-title>Bayesian space-time patterns and climatic determinants of bovine anaplasmosis</article-title>. <source>PLoS ONE.</source> (<year>2016</year>) <volume>11</volume>:<fpage>e0151924</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0151924</pub-id><pub-id pub-id-type="pmid">27003596</pub-id></mixed-citation>
</ref>
<ref id="B15">
<label>15.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Spare</surname> <given-names>MR</given-names></name> <name><surname>Hanzlicek</surname> <given-names>GA</given-names></name> <name><surname>Wootten</surname> <given-names>KL</given-names></name> <name><surname>Anderson</surname> <given-names>GA</given-names></name> <name><surname>Thomson</surname> <given-names>DU</given-names></name> <name><surname>Sanderson</surname> <given-names>MW</given-names></name> <etal/></person-group>. <article-title>Bovine anaplasmosis herd prevalence and management practices as risk-factors associated with herd disease status</article-title>. <source>Vet Parasitol X.</source> (<year>2020</year>) <volume>3</volume>:<fpage>100021</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.vpoa.2019.100021</pub-id><pub-id pub-id-type="pmid">32904721</pub-id></mixed-citation>
</ref>
<ref id="B16">
<label>16.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Binder</surname> <given-names>AM</given-names></name> <name><surname>Armstrong</surname> <given-names>PA</given-names></name></person-group>. <article-title>Increase in reports of tick-borne rickettsial diseases in the United States</article-title>. <source>Am J Nurs.</source> (<year>2019</year>) <volume>119</volume>:<fpage>20</fpage>&#x02013;<lpage>1</lpage>. doi: <pub-id pub-id-type="doi">10.1097/01.NAJ.0000569428.81917.6c</pub-id><pub-id pub-id-type="pmid">31232769</pub-id></mixed-citation>
</ref>
<ref id="B17">
<label>17.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Boorgula</surname> <given-names>GDY</given-names></name> <name><surname>Peterson</surname> <given-names>AT</given-names></name> <name><surname>Foley</surname> <given-names>DH</given-names></name> <name><surname>Ganta</surname> <given-names>RR</given-names></name> <name><surname>Raghavan</surname> <given-names>RK</given-names></name></person-group>. <article-title>Assessing the current and future potential geographic distribution of the American dog tick, Dermacentor variabilis (Say) (Acari: Ixodidae) in North America</article-title>. <source>PLoS ONE.</source> (<year>2020</year>) <volume>15</volume>:<fpage>e0237191</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0237191</pub-id><pub-id pub-id-type="pmid">32776959</pub-id></mixed-citation>
</ref>
<ref id="B18">
<label>18.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raghavan</surname> <given-names>RK</given-names></name> <name><surname>Peterson</surname> <given-names>AT</given-names></name> <name><surname>Cobos</surname> <given-names>ME</given-names></name> <name><surname>Ganta</surname> <given-names>R</given-names></name></person-group>. <article-title>Foley D. Current and future distribution of the Lone Star Tick, <italic>Amblyomma americanum</italic> (L) (Acari: Ixodidae) in North America</article-title>. <source>PLoS ONE</source>. (<year>2019</year>) <volume>14</volume>:<fpage>e0209082</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0209082</pub-id></mixed-citation>
</ref>
<ref id="B19">
<label>19.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raghavan</surname> <given-names>RK</given-names></name> <name><surname>Koestel</surname> <given-names>ZL</given-names></name> <name><surname>Boorgula</surname> <given-names>G</given-names></name> <name><surname>Hroobi</surname> <given-names>A</given-names></name> <name><surname>Ganta</surname> <given-names>R</given-names></name> <name><surname>Harrington</surname> <given-names>J</given-names></name> <etal/></person-group>. <article-title>Unexpected winter questing activity of ticks in the Central Midwestern United States</article-title>. <source>PLoS ONE.</source> (<year>2021</year>) <volume>16</volume>:<fpage>e0259769</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0259769</pub-id><pub-id pub-id-type="pmid">34762706</pub-id></mixed-citation>
</ref>
<ref id="B20">
<label>20.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Dergousoff</surname> <given-names>SJ</given-names></name> <name><surname>Galloway</surname> <given-names>TD</given-names></name> <name><surname>Lindsay</surname> <given-names>LR</given-names></name> <name><surname>Curry</surname> <given-names>PS</given-names></name> <name><surname>Chilton</surname> <given-names>NB</given-names></name></person-group>. <article-title>Range expansion of <italic>Dermacentor variabilis</italic> and <italic>Dermacentor andersoni</italic> (Acari: Ixodidae) near their northern distributional limits</article-title>. <source>J Med Entomol.</source> (<year>2013</year>) <volume>50</volume>:<fpage>510</fpage>&#x02013;<lpage>20</lpage>. doi: <pub-id pub-id-type="doi">10.1603/ME12193</pub-id><pub-id pub-id-type="pmid">23802445</pub-id></mixed-citation>
</ref>
<ref id="B21">
<label>21.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Molaei</surname> <given-names>G</given-names></name> <name><surname>Eisen</surname> <given-names>LM</given-names></name> <name><surname>Price</surname> <given-names>KJ</given-names></name> <name><surname>Eisen</surname> <given-names>RJ</given-names></name></person-group>. <article-title>Range expansion of native and invasive ticks: a looming public health threat</article-title>. <source>J Infect Dis 26.</source> (<year>2022</year>) <volume>226</volume>:<fpage>370</fpage>&#x02013;<lpage>3</lpage>. doi: <pub-id pub-id-type="doi">10.1093/infdis/jiac249</pub-id><pub-id pub-id-type="pmid">35732174</pub-id></mixed-citation>
</ref>
<ref id="B22">
<label>22.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ierardi</surname> <given-names>RA</given-names></name></person-group>. <article-title>A review of bovine anaplasmosis (Anaplasma marginale) with emphasis on epidemiology and diagnostic testing</article-title>. <source>J Vet Diagn Invest</source>. (<year>2025</year>) doi: <pub-id pub-id-type="doi">10.1177/10406387251324180</pub-id><pub-id pub-id-type="pmid">40156087</pub-id></mixed-citation>
</ref>
<ref id="B23">
<label>23.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Kollars TM</surname> <given-names>Jr</given-names></name> <name><surname>Oliver JH</surname> <given-names>Jr</given-names></name> <name><surname>Masters</surname> <given-names>EJ</given-names></name> <name><surname>Kollars</surname> <given-names>PG</given-names></name> <name><surname>Durden</surname> <given-names>LA</given-names></name></person-group>. <article-title>Host utilization and seasonal occurrence of <italic>Dermacentor species</italic> (Acari:Ixodidae) in Missouri, USA</article-title>. <source>Exp Appl Acarol</source>. (<year>2000</year>) <volume>24</volume>:<fpage>631</fpage>&#x02013;<lpage>43</lpage>. doi: <pub-id pub-id-type="doi">10.1023/A:1026566301325</pub-id><pub-id pub-id-type="pmid">11201355</pub-id></mixed-citation>
</ref>
<ref id="B24">
<label>24.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raghavan</surname> <given-names>RK</given-names></name> <name><surname>Neises</surname> <given-names>D</given-names></name> <name><surname>Goodin</surname> <given-names>DG</given-names></name> <name><surname>Andresen</surname> <given-names>DA</given-names></name> <name><surname>Ganta</surname> <given-names>RR</given-names></name></person-group>. <article-title>Bayesian spatio-temporal analysis and geospatial risk factors of human monocytic ehrlichiosis</article-title>. <source>PLoS ONE.</source> (<year>2014</year>) <volume>9</volume>:<fpage>e100850</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0100850</pub-id><pub-id pub-id-type="pmid">24992684</pub-id></mixed-citation>
</ref>
<ref id="B25">
<label>25.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Raghavan</surname> <given-names>RK</given-names></name> <name><surname>Goodin</surname> <given-names>DG</given-names></name> <name><surname>Neises</surname> <given-names>D</given-names></name> <name><surname>Anderson</surname> <given-names>GA</given-names></name> <name><surname>Ganta</surname> <given-names>RR</given-names></name></person-group>. <article-title>Hierarchical Bayesian spatio-temporal analysis of climatic and socio-economic determinants of rocky mountain spotted fever</article-title>. <source>PLoS ONE.</source> (<year>2016</year>) <volume>11</volume>:<fpage>e0150180</fpage>. doi: <pub-id pub-id-type="doi">10.1371/journal.pone.0150180</pub-id><pub-id pub-id-type="pmid">26942604</pub-id></mixed-citation>
</ref>
<ref id="B26">
<label>26.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Curtis</surname> <given-names>AK</given-names></name> <name><surname>Coetzee</surname> <given-names>JF</given-names></name></person-group>. <article-title>Assessment of within-herd seroprevalence of Anaplasma marginale antibodies and associated decreased milk production in an Iowa dairy herd</article-title>. <source>Appl Animal Sci</source>. (<year>2021</year>) <volume>37</volume>:<fpage>126</fpage>&#x02013;<lpage>31</lpage>. doi: <pub-id pub-id-type="doi">10.15232/aas.2020-02110</pub-id></mixed-citation>
</ref>
<ref id="B27">
<label>27.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Lawson</surname> <given-names>AB</given-names></name></person-group>. <source>Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology</source>, 3rd ed. Boca Raton, FL: CRC Press (<year>2018</year>). p. 488. doi: <pub-id pub-id-type="doi">10.1201/9781351271769-1</pub-id></mixed-citation>
</ref>
<ref id="B28">
<label>28.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Enticott</surname> <given-names>G</given-names></name> <name><surname>Ward</surname> <given-names>K</given-names></name> <name><surname>Ashton</surname> <given-names>A</given-names></name> <name><surname>Brunton</surname> <given-names>L</given-names></name> <name><surname>Broughan</surname> <given-names>J</given-names></name></person-group>. <article-title>Mapping the geography of disease: a comparison of epidemiologists&#x02018; and field-level experts&#x00027; disease maps</article-title>. <source>Appl Geogr</source>. (<year>2021</year>) <volume>126</volume>:<fpage>102356</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.apgeog.2020.102356</pub-id></mixed-citation>
</ref>
<ref id="B29">
<label>29.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>MacNab</surname> <given-names>YC</given-names></name></person-group>. <article-title>Bayesian disease mapping: past, present, and future</article-title>. <source>Spat Stat.</source> (<year>2022</year>) <volume>50</volume>:<fpage>100593</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.spasta.2022.100593</pub-id><pub-id pub-id-type="pmid">35075407</pub-id></mixed-citation>
</ref>
<ref id="B30">
<label>30.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Marshall</surname> <given-names>RJ</given-names></name></person-group>. <article-title>Mapping disease and mortality rates using empirical Bayes estimators</article-title>. <source>J R Stat Soc Ser C Appl Stat.</source> (<year>1991</year>) <volume>40</volume>:<fpage>283</fpage>&#x02013;<lpage>94</lpage>. doi: <pub-id pub-id-type="doi">10.2307/2347593</pub-id><pub-id pub-id-type="pmid">12157989</pub-id></mixed-citation>
</ref>
<ref id="B31">
<label>31.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>K&#x000E9;ry</surname> <given-names>M</given-names></name> <name><surname>Schaub</surname> <given-names>M</given-names></name></person-group>. <source>Bayesian Population Analysis Using WinBUGS: A Hierarchical Perspective</source>, 1st ed. Cambridge, MA: Academic Press (<year>2011</year>). p. 554. doi: <pub-id pub-id-type="doi">10.1016/B978-0-12-387020-9.00001-8</pub-id></mixed-citation>
</ref>
<ref id="B32">
<label>32.</label>
<mixed-citation publication-type="book"><person-group person-group-type="author"><name><surname>K&#x000E9;ry</surname> <given-names>M</given-names></name> <name><surname>Royle</surname> <given-names>JA</given-names></name></person-group>. <article-title>Chapter 2. Modeling population dynamics with count data</article-title>. In:<person-group person-group-type="editor"><name><surname>K&#x000E9;ry</surname> <given-names>M</given-names></name> <name><surname>Royle</surname> <given-names>JA</given-names></name></person-group>, editors. <source>Applied Hierarchical Modeling in Ecology: Analysis of Distribution, Abundance and Species Richness in R and BUGS</source>. <publisher-loc>Cambridge, MA</publisher-loc>: <publisher-name>Academic Press</publisher-name>. (<year>2021</year>). p. <fpage>65</fpage>&#x02013;<lpage>156</lpage>. doi: <pub-id pub-id-type="doi">10.1016/B978-0-12-809585-0.00002-8</pub-id></mixed-citation>
</ref>
<ref id="B33">
<label>33.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Royle</surname> <given-names>JA</given-names></name></person-group>. <article-title>N-mixture models for estimating population size from spatially replicated counts</article-title>. <source>Biometrics.</source> (<year>2004</year>) <volume>60</volume>:<fpage>108</fpage>&#x02013;<lpage>15</lpage>. doi: <pub-id pub-id-type="doi">10.1111/j.0006-341X.2004.00142.x</pub-id><pub-id pub-id-type="pmid">15032780</pub-id></mixed-citation>
</ref>
<ref id="B34">
<label>34.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Gelfand</surname> <given-names>AE</given-names></name> <name><surname>Banerjee</surname> <given-names>S</given-names></name> <name><surname>Gamerman</surname> <given-names>D</given-names></name></person-group>. <article-title>Spatial process modelling for univariate and multivariate dynamic spatial data</article-title>. <source>Environmetrics.</source> (<year>2005</year>) <volume>16</volume>:<fpage>465</fpage>&#x02013;<lpage>79</lpage>. doi: <pub-id pub-id-type="doi">10.1002/env.715</pub-id></mixed-citation>
</ref>
<ref id="B35">
<label>35.</label>
<mixed-citation publication-type="web"><source>R2jags: Using R to Run &#x02018;JAGS&#x00027;</source>. Version 0.8-9. 2025. Available online at: <ext-link ext-link-type="uri" xlink:href="https://cran.r-project.org/web/packages/R2jags/index.html">https://cran.r-project.org/web/packages/R2jags/index.html</ext-link> (Accessed May 5, 2025).</mixed-citation>
</ref>
<ref id="B36">
<label>36.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tzala</surname> <given-names>E</given-names></name> <name><surname>Best</surname> <given-names>N</given-names></name></person-group>. <article-title>Bayesian latent variable modelling of multivariate spatio-temporal variation in cancer mortality</article-title>. <source>Stat Methods Med Res.</source> (<year>2008</year>) <volume>17</volume>:<fpage>97</fpage>&#x02013;<lpage>118</lpage>. doi: <pub-id pub-id-type="doi">10.1177/0962280207081243</pub-id><pub-id pub-id-type="pmid">17855747</pub-id></mixed-citation>
</ref>
<ref id="B37">
<label>37.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Ierardi</surname> <given-names>RA</given-names></name> <name><surname>Odemuyiwa</surname> <given-names>SO</given-names></name> <name><surname>Schultz</surname> <given-names>L</given-names></name> <name><surname>Shen</surname> <given-names>Z</given-names></name> <name><surname>Zhang</surname> <given-names>M</given-names></name> <name><surname>Zhang</surname> <given-names>S</given-names></name> <etal/></person-group>. <article-title>Serologic and molecular prevalence of Anaplasma marginale in Missouri beef herds</article-title>. <source>Am J Vet Res.</source> (<year>2025</year>) <volume>86</volume>:<fpage>1</fpage>&#x02013;<lpage>10</lpage>. doi: <pub-id pub-id-type="doi">10.2460/ajvr.25.03.0096</pub-id><pub-id pub-id-type="pmid">40683302</pub-id></mixed-citation>
</ref>
<ref id="B38">
<label>38.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Sandlin</surname> <given-names>CS</given-names></name> <name><surname>Johnson</surname> <given-names>RC</given-names></name> <name><surname>Swaim</surname> <given-names>L</given-names></name> <name><surname>Ashley</surname> <given-names>DL</given-names></name></person-group>. <article-title>Laboratory information management system for emergency response: validation and quality assurance of analytical methodologies</article-title>. <source>SLAS Technol.</source> (<year>2009</year>) <volume>14</volume>:<fpage>126</fpage>&#x02013;<lpage>32</lpage>. doi: <pub-id pub-id-type="doi">10.1016/j.jala.2009.02.001</pub-id></mixed-citation>
</ref>
<ref id="B39">
<label>39.</label>
<mixed-citation publication-type="book"><person-group person-group-type="author"><name><surname>Colangeli</surname> <given-names>P</given-names></name> <name><surname>De Massis</surname> <given-names>F</given-names></name> <name><surname>Cito</surname> <given-names>F</given-names></name> <name><surname>Mercante</surname> <given-names>MT</given-names></name> <name><surname>Ricci</surname> <given-names>L</given-names></name></person-group>. <article-title>Laboratory information management systems: role in veterinary activities</article-title>. In:<person-group person-group-type="editor"><name><surname>Management</surname> <given-names>Association IR</given-names></name></person-group>, editor. <source>Public Health and Welfare: Concepts, Methodologies, Tools, and Applications</source>. <publisher-loc>Palmdale, PA</publisher-loc>: <publisher-name>IGI Global</publisher-name> (<year>2017</year>). p. <fpage>313</fpage>&#x02013;<lpage>26</lpage>. doi: <pub-id pub-id-type="doi">10.4018/978-1-5225-1674-3.ch015</pub-id></mixed-citation>
</ref>
<ref id="B40">
<label>40.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Knorr-Held</surname> <given-names>L</given-names></name> <name><surname>Besag</surname> <given-names>J</given-names></name></person-group>. <article-title>Modelling risk from a disease in time and space</article-title>. <source>Stat Med.</source> (<year>1998</year>) 17:2045&#x02013;60 doi: <pub-id pub-id-type="doi">10.1002/(SICI)1097-0258(19980930)17:18&#x00026;lt;2045::AID-SIM943&#x00026;gt;3.0.CO;2-P</pub-id><pub-id pub-id-type="pmid">9789913</pub-id></mixed-citation>
</ref>
<ref id="B41">
<label>41.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Bernardinelli</surname> <given-names>L</given-names></name> <name><surname>Clayton</surname> <given-names>D</given-names></name> <name><surname>Pascutto</surname> <given-names>C</given-names></name> <name><surname>Montomoli</surname> <given-names>C</given-names></name> <name><surname>Ghislandi</surname> <given-names>M</given-names></name> <name><surname>Songini</surname> <given-names>M</given-names></name></person-group>. <article-title>Bayesian analysis of space&#x02014;time variation in disease risk</article-title>. <source>Stat Med.</source> (<year>1995</year>) <volume>14</volume>:<fpage>2433</fpage>&#x02013;<lpage>43</lpage>. doi: <pub-id pub-id-type="doi">10.1002/sim.4780142112</pub-id><pub-id pub-id-type="pmid">8711279</pub-id></mixed-citation>
</ref>
<ref id="B42">
<label>42.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Banerjee</surname> <given-names>S</given-names></name></person-group>. <article-title>High-dimensional bayesian geostatistics</article-title>. <source>Bayesian Anal.</source> (<year>2017</year>) <volume>12</volume>:<fpage>583</fpage>&#x02013;<lpage>614</lpage>. doi: <pub-id pub-id-type="doi">10.1214/17-BA1056R</pub-id><pub-id pub-id-type="pmid">29391920</pub-id></mixed-citation>
</ref>
<ref id="B43">
<label>43.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Rochlin</surname> <given-names>I</given-names></name> <name><surname>Egizi</surname> <given-names>A</given-names></name> <name><surname>Narvaez</surname> <given-names>Z</given-names></name> <name><surname>Bonilla</surname> <given-names>DL</given-names></name> <name><surname>Gallagher</surname> <given-names>M</given-names></name> <name><surname>Williams</surname> <given-names>GM</given-names></name> <etal/></person-group>. <article-title>Microhabitat modeling of the invasive Asian longhorned tick (Haemaphysalis longicornis) in New Jersey, USA</article-title>. <source>Ticks Tick Borne Dis.</source> (<year>2023</year>) <volume>14</volume>:<fpage>102126</fpage>. doi: <pub-id pub-id-type="doi">10.1016/j.ttbdis.2023.102126</pub-id><pub-id pub-id-type="pmid">36682197</pub-id></mixed-citation>
</ref>
<ref id="B44">
<label>44.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Noden</surname> <given-names>BH</given-names></name> <name><surname>Tanner</surname> <given-names>EP</given-names></name> <name><surname>Polo</surname> <given-names>JA</given-names></name> <name><surname>Fuhlendorf</surname> <given-names>SD</given-names></name></person-group>. <article-title>Invasive woody plants as foci of tick-borne pathogens: eastern redcedar in the southern Great Plains</article-title>. <source>J Vector Ecol</source>. (<year>2021</year>) 46:12&#x02013;18, 7. doi: <pub-id pub-id-type="doi">10.52707/1081-1710-46.1.12</pub-id><pub-id pub-id-type="pmid">35229576</pub-id></mixed-citation>
</ref>
<ref id="B45">
<label>45.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Patrick</surname> <given-names>CD</given-names></name> <name><surname>Hair</surname> <given-names>JA</given-names></name></person-group>. <article-title>White-tailed deer utilization of three different habitats and its influence on lone star tick populations</article-title>. <source>J Parasitol.</source> (<year>1978</year>) <volume>64</volume>:<fpage>1100</fpage>&#x02013;<lpage>6</lpage>. doi: <pub-id pub-id-type="doi">10.2307/3279735</pub-id></mixed-citation>
</ref>
<ref id="B46">
<label>46.</label>
<mixed-citation publication-type="web"><collab>United States Department of Agriculture National Agricultural Statistics Service (USDA-NASS)</collab>. <source>Quick Stats (Cattle, Cows, Beef - Inventory, Total)</source>. Available online at: <ext-link ext-link-type="uri" xlink:href="https://quickstats.nass.usda.gov/">https://quickstats.nass.usda.gov/</ext-link> (Accessed March 6, 2025).</mixed-citation>
</ref>
<ref id="B47">
<label>47.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hrozencik</surname> <given-names>RA</given-names></name></person-group>. <source>Drought conditions and change in U.S. beef cattle herd size</source>, <fpage>2000</fpage>&#x02013;<lpage>2023</lpage> (<year>2024</year>). United States Department of Agriculture Economic Research Service. Source: USDA, Economic Research Service using data from the U.S. Drought Monitor and USDA, National Agricultural Statistics Service.</mixed-citation>
</ref>
<ref id="B48">
<label>48.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hairgrove</surname> <given-names>TB</given-names></name> <name><surname>Craig</surname> <given-names>TM</given-names></name> <name><surname>Budke</surname> <given-names>CM</given-names></name> <name><surname>Rodgers</surname> <given-names>SJ</given-names></name> <name><surname>Gill</surname> <given-names>RJ</given-names></name></person-group>. <article-title>Seroprevalence of Anaplasma marginale in Texas cattle</article-title>. <source>Prev Vet Med.</source> (<year>2014</year>) <volume>116</volume>:<fpage>188</fpage>&#x02013;<lpage>92</lpage>. doi: <pub-id pub-id-type="doi">10.1016/j.prevetmed.2014.05.008</pub-id><pub-id pub-id-type="pmid">24931130</pub-id></mixed-citation>
</ref>
<ref id="B49">
<label>49.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Jones</surname> <given-names>CJ</given-names></name> <name><surname>Kitron</surname> <given-names>UD</given-names></name></person-group>. <article-title>Populations of <italic>Ixodes scapularis</italic> (Acari: Ixodidae) Are modulated by drought at a lyme disease focus in illinois</article-title>. <source>J Med Entomol.</source> (<year>2000</year>) <volume>37</volume>:<fpage>408</fpage>&#x02013;<lpage>15</lpage>. doi: <pub-id pub-id-type="doi">10.1093/jmedent/37.3.408</pub-id><pub-id pub-id-type="pmid">15535585</pub-id></mixed-citation>
</ref>
<ref id="B50">
<label>50.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Nielebeck</surname> <given-names>C</given-names></name> <name><surname>Kim</surname> <given-names>SH</given-names></name> <name><surname>Pepe</surname> <given-names>A</given-names></name> <name><surname>Himes</surname> <given-names>L</given-names></name> <name><surname>Miller</surname> <given-names>Z</given-names></name> <name><surname>Zummo</surname> <given-names>S</given-names></name> <etal/></person-group>. <article-title>Climatic stress decreases tick survival but increases rate of host-seeking behavior</article-title>. <source>Ecosphere.</source> (<year>2023</year>) <volume>14</volume>:<fpage>e4369</fpage>. doi: <pub-id pub-id-type="doi">10.1002/ecs2.4369</pub-id></mixed-citation>
</ref>
<ref id="B51">
<label>51.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hefley</surname> <given-names>TJ</given-names></name> <name><surname>Hooten</surname> <given-names>MB</given-names></name> <name><surname>Russell</surname> <given-names>RE</given-names></name> <name><surname>Walsh</surname> <given-names>DP</given-names></name> <name><surname>Powell</surname> <given-names>JA</given-names></name></person-group>. <article-title>When mechanism matters: Bayesian forecasting using models of ecological diffusion</article-title>. <source>Ecol Lett.</source> (<year>2017</year>) <volume>20</volume>:<fpage>640</fpage>&#x02013;<lpage>50</lpage>. doi: <pub-id pub-id-type="doi">10.1111/ele.12763</pub-id><pub-id pub-id-type="pmid">28371055</pub-id></mixed-citation>
</ref>
<ref id="B52">
<label>52.</label>
<mixed-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Tao</surname> <given-names>Y</given-names></name> <name><surname>Hite</surname> <given-names>JL</given-names></name> <name><surname>Lafferty</surname> <given-names>KD</given-names></name> <name><surname>Earn</surname> <given-names>DJD</given-names></name> <name><surname>Bharti</surname> <given-names>N</given-names></name></person-group>. <article-title>Transient disease dynamics across ecological scales</article-title>. <source>Theor Ecol</source>. (<year>2021</year>) <volume>14</volume>:<fpage>625</fpage>&#x02013;<lpage>40</lpage>. doi: <pub-id pub-id-type="doi">10.1007/s12080-021-00514-w</pub-id><pub-id pub-id-type="pmid">34075317</pub-id></mixed-citation>
</ref>
</ref-list>
<fn-group>
<fn fn-type="custom" custom-type="edited-by" id="fn0001">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1126703/overview">Gabriele Maier</ext-link>, University of California, Davis, Davis, United States</p>
</fn>
<fn fn-type="custom" custom-type="reviewed-by" id="fn0002">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1815260/overview">Carlos Gonz&#x000E1;lez-Crespo</ext-link>, University of California, Davis, Davis, United States</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3148343/overview">Terry Engelken</ext-link>, Iowa State University, United States</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3207818/overview">Shih-Yu Chen</ext-link>, University of California, Davis, Davis, United States</p>
</fn>
</fn-group>
</back>
</article> 