In many developed countries, the average person has very little or no contact with livestock, yet there is undoubtedly a risk of infectious agent transmission between livestock and human populations through the food supply chain and environmental intermediaries. Antimicrobial-resistant pathogens are capable of moving between animal and human populations via these pathways. Bacterial gene sequencing and multi-locus sequence typing suggest that whole bacterium transfer has occurred between at least poultry meat and humans (Overdevest et al., 2011; Kluytmans et al., 2013) and plasmid restriction-enzyme typing shows horizontal gene transfer of resistance elements between animal and human strains (Yan et al., 2004). Additionally, a recent metagenomic study on human feces found a higher prevalence of resistance genes to antimicrobials used in both animals and humans than resistance to human-limited antimicrobials (Forslund et al., 2013).

Consumers are therefore concerned about antimicrobial use in livestock and the risk of antimicrobial resistance spreading from livestock to humans by the consumption of animal products. Companies such as McDonalds, Tyson Foods, and Chipotle have responded with public commitments to limit or eliminate antimicrobials used in livestock in their supply chains (Chipotle, 2013; Tyson Foods, 2015; McDonalds, 2016). The Food and Drug Administration recently limited the use of medically-important antimicrobials in livestock for production purposes (i.e., growth promotion) and required veterinary oversight for antimicrobial use (US Food and Drug Administration, 2012, 2013). However, it is unrealistic to think that antimicrobials can be completely phased out of animal agriculture. Antimicrobials will continue to play a vital role in keeping livestock healthy and producing animal products efficiently and sustainably for a growing human population.

We must therefore devise antimicrobial stewardship policies to reduce the risk of antimicrobial resistance spread from livestock to humans. One possibility is to modify withdrawal periods required after antimicrobial use in livestock to account for resistance dynamics (Volkova et al., 2016). Antimicrobials used in livestock are already subject to meat and milk withdrawal times to prevent violative levels of drug residues from entering the human food supply. These withdrawal periods vary by country and by antimicrobial indication, varying from 0 to 10 days for oral chlortetracycline (P.R. Vademecum¹; Hoffmann La-Roche Inc., 1997; Canadian Food Inspection Agency, 2014; Australian Pesticides and Veterinary Medicines Authority, 2015; Zoetis, 2016; EU Directorate General Health Consumers, 2017; New Zealand Ministry for Primary Industries, 2017; UK Veterinary Medicines Directorate, 2017). “Resistance withdrawals” could be used to decrease the prevalence of resistant bacteria and genes in an animal's enteric microbiome before it is sent for slaughter, where enteric bacteria can contaminate meat products (De Filippis et al., 2013).

In order to investigate the efficacy and length of resistance withdrawal periods that would reduce the prevalence of resistance in the livestock enteric microbiota, we built a model of the pharmacokinetics-pharmacodynamics of chlortetracycline (CTC) fed to beef steers, and the population dynamics of their enteric generic Escherichia coli. Chlortetracycline is a commonly used antimicrobial on beef feedlots (United States Department of Agriculture, 2013), and tetracyclines were identified as a highly important antimicrobial class for human medicine by the FDA (US Food Drug Administration, 2003), making CTC a suitable candidate for evaluating the impact of antimicrobial resistance withdrawal periods.

The model consists of 3 sub-models that were connected and parameterized for CTC and generic E. coli in beef cattle: a pharmacokinetic model for the concentrations of orally administered drugs in the gastrointestinal tract (Cazer et al., 2014), a bacterial population dynamics model, and a pharmacodynamic model (Ayscue et al., 2009; Volkova et al., 2012). The framework for connecting these models and using them to investigate resistance withdrawal periods has been described (Volkova et al., 2016). Each model is described briefly below. Model equations are listed in Table 1. Each parameter was considered to be either a constant or a random variable. Each simulation of the three connected models represents one realization of a treated animal, with the values of the random variables drawn from the animal population-level parameter distributions. The model was parameterized using data available from literature wherever possible. For a parameter with only two published estimates, a Uniform distribution was used with the estimates as the maximum and minimum. For a parameter with only one published estimate, a Uniform distribution with the maximum and minimum being ±25% of the estimate was assigned (Volkova et al., 2017). For a parameter with at least 3 published estimates, the parameter distribution was determined by fitting candidate distributions to the dataset of the published estimates of the parameter values, with PROC CAPABILITY in SAS® 9.4 software for Windows (SAS Institute Inc., Cary, NC, U.S.); the best-fit distribution for the parameter was selected using goodness-of-fit tests (Anderson-Darling and Kolmogorov-Smirnov) and visual examination of quantile-quantile plots. The parameter distributions used in the model simulations are listed in Table 2. (The data used to fit the parameter value distributions for the parameters with at least 3 published estimates are included in Supplementary Materials).

All three scenarios of CTC indications for beef cattle (antimicrobial liver abscess reduction—ARLA; disease control—ADC; disease treatment—ADT) were implemented in the model of CTC pharmacokinetics-pharmacodynamics and generic E. coli population dynamics in the bovine large intestine. The average CTC concentration in the large intestine during treatment was calculated for the median steer, 5th percentile steer, and 95th percentile steer. For ARLA, the median steer had an average large intestine CTC concentration of 0.22 μg/mL, the 5th percentile steer had a concentration of 0.06 μg/mL, and the 95th percentile steer had a concentration of 0.62 μg/mL. For steers given ADC, the averages were 1.17, 0.34, and 2.96 μg/mL for median, 5th percentile and 95th percentile, and for ADT the average CTC concentrations were 12.99, 3.70, and 34.12 μg/mL, respectively. This is consistent with the results from our previous deterministic pharmacokinetic model (Cazer et al., 2014).

The use of CTC for any indication resulted in an increase in the median proportion (Figures 1D,G,J) and absolute number (Figure S1) of resistant E. coli during treatment in 1,000 simulated cattle. The median proportion resistant was 38% before treatment and increased to 46% at the end of ARLA, 60% at the end of ADC, and 66% at the end of ADT. In terms of the number of resistant E. coli in the large intestine, there were 10^5.76 CFU/g before treatment, 10^5.82 CFU/g at the end of ARLA, 10^5.93 CFU/g at the end of ADC, and 10^5.89 CFU/g at the end of ADT. The median proportion of intermediate E. coli also increased during ARLA (10% at the end of treatment) and ADC (11%) but decreased during ADT (5%) relative to pre-treatment levels (8%) (Figures 1B,E,H,K). However ADT still greatly increased the median proportion (71% at the end of ADT) and amount (10^5.92 CFU/g) (Figure S1) of non-susceptible bacteria compared to before treatment (46%; 10^5.84 CFU/g), accompanying the drop in the median proportion of susceptible E. coli (54% before treatment and 29% at the end of ADT) (Figure 1L). The proportions and amounts of resistant, intermediate, and susceptible bacteria reached an approximate steady state during ARLA and ADC (Figures 1D,G; Figure S1), whereas a steady state was not reached during the shorter ADT and the proportion of resistance peaked, on average, on the second day after ADT treatment was discontinued (Figure 1J). In general, ARLA and ADC resulted in an upward shift of the median and upper limit (95%) of the proportion non-susceptible distribution but little change in the lower limit (5%) during antimicrobial treatment (Figures 1F,I). In contrast, during the ADT period and following 3 days the entire proportion resistant distribution shifted upwards (Figure 1J).

The median proportion of resistant E. coli reversed to the pre-treatment median confidence interval 15 days after ARLA ended, 31 days after ADC ended, and 36 days after ADT ended (Figures 1B–D). Only 35% of ARLA cattle, 50% of ADC cattle and 61% of ADT cattle returned to within 10% of their individual pre-treatment resistant E. coli proportion by the end of the 90 day simulation period. This includes 18% of ARLA cattle, 9% of ADC cattle, and 6% of ADT cattle that were already within 10% of pre-treatment levels at the end of antimicrobial treatment. Among the individual cattle that did return to pre-treatment levels, the median time from the end of treatment to the resistance reversion was significantly different between the treatment groups (P < 0.001): <1 day (mean 6 days) following ARLA, 8 days (mean 11 days) following ADC, and 11 days (mean 15 days) following ADT. Since ADT duration is shorter, the 90 day simulation period captured 60 days post-ARLA and -ADC but it captured 83 days post-ADT. At 60 days post-treatment, 59% of ADT cattle had returned to within 10% of pre-treatment proportion resistant with a median return time of 11 days (mean 14 days) after the treatment.

In the absence of treatment, 38% of generic E. coli in the cattle large intestine were resistant, 8% intermediate, and 54% susceptible to CTC on average (Figure 2). There was no significant difference in the average proportions of resistant bacteria during ADC (58%) and ADT (59%) (P = 0.850, Figure 2A), but ADC had a significantly higher proportion of intermediate bacteria (12%) compared to ADT (6%) (P < 0.001) (Figure 2B). This was associated with ADC having a lower average susceptible proportion of E. coli (30%) than ADT (35%, Figure 2C) despite ADT having the highest maximum proportion resistant (72%). At the steady state during ARLA, 46% of E. coli were resistant, 10% intermediate, and 44% susceptible on average. The average proportion of resistant E. coli during any of the three CTC treatments was significantly different from that in the absence of treatment (38%) (P < 0.001, Figure 2A). By the end of the 90 day simulation period, the mean proportion resistant reversed and was not significantly different from that in the absence of treatment (P > 0.050, Figure 2A).

Brand-name U.S. CTC feed products have a 0-day meat withdrawal period for beef cattle so they can be sent to slaughter immediately after the consumption of CTC. We assumed that 6 h elapse between leaving the feedlot and slaughter. The median cattle given ARLA had 46% resistant enteric E. coli at slaughter; the median ADC cattle had 60% resistant E. coli, and the median ADT cattle had 67% resistant E. coli (Figure 3). Generic U.S. CTC products have a 2-day withdrawal period following ADC and a 1-day withdrawal period following ADT. These withdrawals resulted in statistically significant different proportions of resistant E. coli at slaughter compared to the 0-day withdrawal: the median cattle had 58% resistant E. coli at 2 days after ADC (P = 0.012) and 71% resistant 1 day after ADT (P < 0.001) (Figure 3). The cattle treated with CTC had a wider distribution and greater maximum proportion resistant at the currently recommended withdrawal times compared to those in the absence of treatment (Figure 3). The lower bound of the resistance distribution at the withdrawal times was higher for ADT relative to the other two treatments (Figure 3).

Before and after CTC treatments, the proportions of CTC resistant, intermediate, and susceptible enteric E. coli in the large intestine were sensitive to variability in the inflowing E. coli distribution of resistance (p_j). During the treatments, the proportions were sensitive to variability in the bacterial population dynamics parameters and in the CTC pharmacokinetic-pharmacodynamic parameters (Figure 4, Spearman coefficients smaller than the Bonferroni corrected α = 0.0006 are shown). In general, higher CTC dosages made the proportions less sensitive to the distribution of resistance in the inflowing E. coli but more sensitive to the overall inflow rate (λ_in) (Figure 4). In addition to the inflow rate and the inflow resistance distribution, the proportions during ADT were sensitive to the starting proportions (start_j) and the CTC minimum inhibitory concentration (MIC) for the resistant E. coli. Conversely, the proportions during ARLA and ADC were sensitive to the MIC for the susceptible E. coli. Variability in the following pharmacokinetic parameters had a significant impact on the E. coli proportions only during ARLA and ADC (Figures 4A,C): CTC abiotic degradation throughout the gastrointestinal tract and other organs (δ), CTC binding to the digesta in the large intestine (η), and volume of the digesta in the large intestine (V_li). Variability in the Hill coefficient (H_j), a pharmacodynamic parameter, had no significant impact on the E. coli proportions during treatments. Variability in the bacterial population dynamics parameters of the growth rate (r), resistance fitness cost (α), carrying capacity (N_max), and the resistance horizontal transfer rate (β), plus the pharmacokinetic parameters of the CTC flow rates through the gastrointestinal compartments (γ_s, γ_{upper_si}, γ_{rest_si}, γ_li) and the fraction excreted in bile (E_b), had no significant effect on the proportions of resistant, intermediate, and susceptible E. coli during treatments.

Despite modeling a long follow-up period after ending CTC treatment (60 days after ARLA and ADC, 83 days after ADT), a significant number of the simulated cattle had still not returned to their pre-treatment proportion of resistant E. coli after CTC treatment. The dosage of CTC appeared to be associated with the percent of cattle that returned to their pre-treatment levels, with higher dosages (ADT, ADC) having greater proportions of cattle returning to pre-treatment resistance than low-dosage ARLA. This suggests that the low-dosage long-term ARLA may more frequently shift the enteric E. coli equilibrium to a state that is stable in the absence of CTC. This is evident in the change in proportion resistant from the end of treatment to the end of the simulation period (day 90). ARLA cattle that never returned to pre-treatment levels (65% of ARLA cattle) had a median difference in proportion resistant of 1.7% from the end of ARLA to day 90, indicating that they had reached an equilibrium during treatment that was relatively stable in the absence of CTC. On the other hand, ARLA cattle that did return to pre-treatment levels (35% of ARLA cattle) had a larger median change in proportion resistant (6.4%) from the end of treatment to the end of the simulation period. It is possible that the high levels of resistance observed during ADT and ADC were unsustainable after treatment given the model parameters (particularly the resistant inflow proportion). Only 2.4% of ADC cattle and 4.9% of ADT cattle achieved an equilibrium during treatment that was relatively stable in the absence of CTC (<1.7% difference between end of treatment and day 90 proportion resistant). However, the ARLA cattle that returned to their pre-treatment levels did so much faster than ADC and ADT cattle, likely because there was a smaller change in resistance level from pre-treatment to the end of ARLA (Figure 1).

Additional investigation is needed to study the impact of treatment duration separately from dosage, including testing off-label ADT treatment durations. Pulse-therapy with ADT dosages (3 treatments, 1 day apart) has been implemented in a beef cattle field study; an approximate steady state of 80% resistant E. coli isolates was reached by the second treatment (double the pre-treatment proportion of 40%) (Platt et al., 2008). This is similar to the mean pre-treatment proportion resistant (38%) and the mean maximum proportion resistant after ADT (72%) in our study. At the end of the 17 day post-treatment follow-up period, the proportion of resistant isolates in that study was still 1.5 times greater than the pre-treatment proportion. If the decrease continued at the same rate, the proportion resistant would reverse to the pre-treatment level 34 days after the treatment ended, similar to the 36 days required in our model for the median proportion resistant to be within 10% of the pre-treatment median. Additionally, the average proportion resistant during ADT in our study (59%) fell within the 95% confidence interval of the average proportion resistant during ADT pulse-therapy (58.7–77.3%) (Platt et al., 2008), confirming that our model is projecting biologically plausible resistance dynamics.

Unfortunately it is difficult to compare our model results to the data from field trials on E. coli tetracycline resistance prevalence following CTC treatment due to the variable field study design and management conditions. Those include pooling of isolates across treatment groups and time (Alexander et al., 2008), combination antimicrobial therapy (Kanwar et al., 2013), and reporting of animal-level rather than isolate-level results (Sharma et al., 2008). In order to fully validate the resistance prevalence predictions of this model, field studies are required that sample individual animals, determine the prevalence of tetracycline resistant E. coli isolates before and at several points after CTC treatment, and do not alter diet or environmental conditions during the study period.

This model illustrated important differences in individual and population level antimicrobial resistance. Each simulated population of 1,000 cattle reached its pre-treatment population distribution of tetracycline resistance within the follow-up period (Figure 1). This return occurred approximately 2 weeks after ARLA and 4–5 weeks after ADC or ADT ended. Even though the resistance levels of many individual animals were still significantly altered by CTC treatment, the population or herd resistance was able to return to its initial distribution. This implies that there would be no net increase in resistance exported from the feedlot to slaughterhouses if a sufficient antimicrobial resistance withdrawal period was applied.

The resistance dynamics following different dosages should be considered in antimicrobial use policies. When Denmark stopped using growth promoting doses of antimicrobials (like ARLA) in weaner pigs, the amount of antimicrobials used for disease treatment (like ADT) increased due to higher disease incidence (Kjeldsen and Callesen, 2006). A similar change in the use of CTC may result in significant increases in resistance exported from farms to slaughterhouses, depending on disease incidence and CTC withdrawal period before slaughter. However, long-term ARLA or ADC may release significantly more resistant E. coli, cumulatively, into the feedlot environment compared to one 5-day course of ADT. This highlights the need for additional rigorous, longitudinal trials comparing CTC labeled uses and collecting data on E. coli in cattle, in the feedlot environment, and on beef products.

Based on the model outcomes, it is evident that the current U.S. withdrawal periods (designed to mitigate violative drug residues in the edible meat) for in-feed CTC (Zoetis Aureomycin 50; ChlorMax 50; Hoffmann La-Roche Inc., 1997) in beef cattle are insufficient to reduce the treatment-associated prevalence of resistant E. coli in the large intestine, which can contaminate processing plants and beef products at slaughter (Sheridan, 1998; Aslam et al., 2003). Currently, U.S. cattle can consume CTC until immediately prior to slaughter and hence the proportion of tetracycline resistant bacteria in their intestine is significantly greater than in untreated cattle (Figure 3). The 24-h withdrawal after ADT may further increase the proportion of resistant E. coli at slaughter because of the CTC intestinal transit times.

Apart from the United States, the only other country with a large beef cattle industry that permits the use of oral CTC is Canada. They allow CTC fed at 70 mg/head per day (ARLA dosage) to prevent foot rot in beef cattle with a pre-slaughter withdrawal period of 5 days (Canadian Food Inspection Agency, 2016). Canada also has an approved CTC-sulfamethazine combination product that is fed at 350 mg CTC per head per day (ADC dosage) with a 10 day pre-slaughter withdrawal period (Canadian Food Inspection Agency, 2016). The European Union, United Kingdom, Australia, New Zealand, Brazil, Argentina, and Mexico have no approved oral CTC products for beef cattle over 6 months old, although a few permit topical CTC sprays with a 0 day pre-slaughter withdrawal period and New Zealand has an approved intrauterine CTC product with a 7 day pre-slaughter withdrawal period (P.R. Vademecum¹; Australian Pesticides and Veterinary Medicines Authority, 2015; EU Directorate General Health Consumers, 2017; New Zealand Ministry for Primary Industries, 2017; UK Veterinary Medicines Directorate, 2017). This modeling study demonstrated that a 15 day withdrawal after ARLA, a 31 day withdrawal after ADC, and a 36 day withdrawal after ADT (Figure 1) may be necessary to reduce the median prevalence of tetracycline resistance among enteric E. coli that could contaminate beef products. Such withdrawal periods would be longer than any current CTC withdrawal periods (which are currently used to control only the CTC residues in the animal edible tissues) in countries with large beef industries. Similar or longer withdrawal periods have been used in antimicrobial feeding studies without detriment to cattle health and welfare (Alexander et al., 2008; Sharma et al., 2008; Agga et al., 2016). However, the economic and welfare costs of resistance withdrawal periods will depend on the specific disease treated and management strategy.

The same field studies (Alexander et al., 2008; Agga et al., 2016) did not find the current withdrawal periods effective in decreasing tetracycline resistance levels. However, one study (Alexander et al., 2008) observed a large increase in tetracycline resistant fecal E. coli when switching from a silage to grain based diet and this effect overwhelmed the ability to detect any changes due to antimicrobial withdrawal. The second study (Agga et al., 2016) found a decrease in fecal E. coli tetracycline resistance during a 27-day withdrawal after ADT but then observed a steady increase in both control and treated groups for an additional 90 days. They concluded that resistance is selected for in cattle-occupied pens independently of antimicrobial use (Agga et al., 2016). Since our model includes only effects of the administered antimicrobials, it is unable to simulate the pattern they observed. The model could be expanded to include the effects of diet (Alexander et al., 2008; Volkova et al., 2016, 2017), environmental E. coli populations (Ayscue et al., 2009; Volkova et al., 2013), environmental contamination with antimicrobial drugs (Call et al., 2013), and animal feeding or environmental contamination with other antimicrobial compounds such as heavy metals (Berendonk et al., 2015).

The sensitivity of the outputs of our model to E. coli population dynamics parameters, particularly the inflow and outflow of E. coli in the large intestine, emphasizes the lack of knowledge about E. coli and antimicrobial resistance circulation in feedlot environments. It also suggests that interventions aimed at changing the turnover of E. coli in the large intestine and the incoming proportions of resistant bacteria may be highly effective at reducing antimicrobial resistance. For example, moving cattle to a previously unoccupied pen for the resistance withdrawal period may reduce the ingestion of resistant bacteria (Agga et al., 2016) and shift the enteric population to a lower-resistance equilibrium. Additional research is needed on the circulation of antimicrobial resistant bacteria and genes in the feedlot environment and how the environmental bacterial populations intersect with the enteric ones. Probiotics and some feed additives have been shown to alter E. coli O157 dynamics in beef cattle (Sargeant et al., 2007) and similar strategies could complement an antimicrobial withdrawal period. Altering pharmacokinetic parameters, such as CTC degradation rate in the gastrointestinal tract or its sorption to digesta, may also be an avenue for decreasing the antimicrobial exposure of enteric microbiomes.

The level of resistant bacteria during CTC treatment was not significantly associated with the fitness cost value or the plasmid transfer rate value in the global sensitivity analysis. These findings are consistent with mathematical models of tetracycline resistant E. coli in the swine intestine, which found that the effect of the plasmid transfer rate was inconsequential compared to the effect of the growth rate of resistant bacteria (Graesboll et al., 2014; Ahmad et al., 2015a). The same models also found that resistant bacteria could persist in the swine intestine with a fitness cost up to an 80% reduction in the growth rate (Graesboll et al., 2014), although this was much greater than the fitness cost they observed in vitro (Ahmad et al., 2015b). Consistent with our model of tetracycline resistance in E. coli in the cattle intestine, the models of tetracycline resistant E. coli in the swine intestine found that bacterial inflow and outflow had a stronger correlation with the level of resistance during treatment than fitness cost or plasmid transfer rates (Graesboll et al., 2014).

By necessity, mathematical models are a simplified representation of biologic systems and can omit confounding or integral parameters. Since our model was limited to modeling E. coli within the large intestine, we were unable to directly account for environmental factors that may impact resistance dissemination and persistence in beef feedlots. In addition, this model did not account for co-selection of CTC resistance as a result of administering other antimicrobials, which may be an important mechanism for resistance dissemination and persistence in food animals (Love et al., 2016). The model parameter value distributions were assigned based on the available published literature. However, specific estimates of the relevant parameters for E. coli and CTC in cattle are often lacking and the parameter value distributions built on sparse data from cattle and other species introduce an unknown amount of error into the model outputs. In addition, in vitro data were used when in vivo data were not available for parameterization. This should be considered when interpreting the model outputs. For example, two in vitro estimates of tetracycline fitness cost in E. coli were used to parameterize fitness cost in our model (Nguyen et al., 1989; Ahmad et al., 2015b), resulting in a narrow range of fitness cost values (Table 2B). We performed additional model simulations considering all biologically possible values of fitness cost by specifying Uniform (0, 0.99) for the fitness cost parameter (data not shown). In that case, the median withdrawal period for ADT decreases from 36 days to 12 days.

In conclusion, our model of CTC pharmacokinetics-pharmacodynamics and the enteric bacterial population dynamics in beef cattle demonstrated that a withdrawal period before slaughter can be effective in reducing the population distribution of tetracycline resistant E. coli to pre-treatment levels. However, the withdrawal periods necessary to mitigate this microbiological food safety risk are significantly longer than current CTC withdrawal periods designed to mitigate toxicological food safety risks. The dynamics of resistant E. coli during and after CTC treatment vary by CTC dosage.

CC developed the chlortetracycline pharmacokinetic model, adapted the other model components for this research, parameterized the model, edited the MatLab code, analyzed the model outputs, and drafted this manuscript. LD adapted model components for chlortetracycline pharmacodynamics and tetracycline-resistant Escherichia coli in cattle, wrote the MatLab code, and revised this manuscript. VV developed the pharmacodynamic and Escherichia coli population models, contributed to the pharmacokinetic model development and model parameterization, and revised this manuscript. YG contributed to the development of the models, model parameterization, model output analysis, and revised this manuscript.