The data used in this study was obtained from the World Health Organization (WHO) which had public data from 195 countries for the period, 2000–2017 (http://apps.who.int/gho/data/view.main.ghe1002015-CH3?lang=en). The raw data was available at the country level, and the analysis has been conducted at the country level.

We determined the modeling strategy for each country based on the quality and availability of data. This study analyzed the DRM information of 13,541,989 children under five. The worldwide spatial pattern of deaths caused by diarrheal diseases was analyzed using GIS and Moran's I, Getis-Ord Gi, Mean Center, and Standard Deviational Ellipse (SDE).

The global spatial autocorrelation statistical methodology was used to measure the correlations in regional observations, find patterns, and determine the levels of spatial clustering among neighboring countries (13). Also, we utilized the spatial weight matrix construction in spatial autocorrelation for data analysis as a spatial weights matrix file (.swm). It compared the values of variables in a single location with those in other locations (14, 15). It was calculated as follows:

Where N was the number of patients, Xi was the value of the variable in a certain location, Xj was the value of the variable in another location, X was the mean of the variable, and Wij was the weight used for comparing locations i and j. Wij was a weighted matrix based on distance, and it was the reversed distance between locations i and j (16).

When values for two neighboring features are either both larger than the mean or both smaller than the mean, the cross-product will be positive. When one value is smaller than the mean and the other value larger, then the cross-product will be negative. In all instances, the higher the deflection from the average, the larger the cross-product effect. If the values in the dataset tend to cluster spatially (high values cluster near other high values; low values cluster near other low values), the Moran's Index will be positive. When high values repel other high values and tend to be near low values, the Index will be negative. If positive cross-product values balance negative cross-product values, the Index will be near zero. The numerator is normalized by the variance so that Index values fall between −1.0 and +1.0. The local Gi^*(d) statistic (local G-statistic) is used to test the statistical significance of localized clusters (i.e., related to leading causes of death), and to establish the spatial extent of these clusters (17). The local G-statistic is useful for identifying individual members of local clusters by determining the spatial dependence and relative magnitude between an observation and its neighboring observations (18). The equation for calculating the local G-statistic is as follows:

Where Wij (d) is the spatial weight vector that defines values for location j (within the distance of d) from neighboring location i. W^*i is the sum of the weights Wij, S^*1i is the square sum of the weights, and S^* is the standard deviation of data in the locations and, n is the number of cases (16).

Getis-Ord Gi^* recognizes statistically significant spatial clusters of high values (hotspots) and low values (cold spots). It creates an Output Feature Class with a z-score, p-value, and confidence level bin (Gi_Bin) for each feature in the Input Feature Class.

The Mean Center is the average x coordinate and y coordinate for all features in the geographical area being studied. It is useful for tracking changes in the diffusion or for comparing the diffusions of various types of features (16):

It is determined by:

Where x_i and y_i are the peculiarities for distinguishing feature i, and n is the sum of the feature.

The Weighted Mean Center is calculated using:

Where w_iis the weight of distinguishing featurei.

Furthermore, to calculate the center (c) for a 3rd aspect if a z attribute exists for each distinguishing feature, the following equation is used:

A usual way of measuring the trend of a prevalent disease among the population is to calculate the standard distance separately in the x and y coordinates. These two measures define the axis of an ellipse encompassing the distribution of features. It is referred to as the Standard Deviational Ellipse (SDE), as the method calculates the standard deviation of the x coordinates and y coordinates from the Mean Center to define the axis of the ellipse. The ellipse allows us to see if the distribution of the features is elongated and determine if it has a particular orientation. Graphing ellipses for disease-related deaths such as diarrhea surveillance programs can, over time, potentially offer real-time outcomes of its spatial spread trend, as researchers continue their focus on the central trends and diffusion patterns.

The SDE is determined by:

Where x_i and y_i are the coordinates for feature i, {X-,Y-} represents the Mean Center for the features, and n is the sum of the feature.

The angle of rotation is calculated as:

Where x-iand yi-are the deviations of the xycoordinates from the Mean Center.

The standard deviations for the x axis and yaxis are:

The Moran's I value of 0.05 (p < 0.001) for the year 2000 demonstrated that there was a notable clustering of DRM in children under five all over the world. A z-score of 3.12 confirmed that there was less than a 1% probability that this clustered pattern of DRM could be entirely the result of random chance Figure 1A. Therefore, it was widely prevalent in 195 countries worldwide. The results also showed that Moran's I for the clustering process during the period 2000–2017 increased from 0.05 to 0.06 (Figure 1). This indicated the formation of highly concentrated clusters of deaths from diarrheal disease worldwide (Figure 1).

The Getis-Ord Gi^* hotspot analysis recognized neighboring hotspots in Asia and Africa. The DRM in children under five was not randomly distributed (Figure 2). The overlap of the cluster areas of diffused DRM was noted, pointing perhaps to a co-factor in the area.

Figure 2 shows the DRM's Mean Center calculated for the world countries from 2000 to 2017. The results demonstrated that the Mean Center was in India for the years 2000 to 2010, and included most Asian countries (India, Nepal, Bangladesh, Myanmar, Afghanistan, Yemen, Uzbekistan, Kazakhstan, and Sri Lanka). The Standard Deviational Ellipse also had a northwest-southeast direction. However, from 2011 onwards, the average DRM has shifted to African countries (Nigeria, Cameroon, Equatorial Guinea, Gabon, Republic of the Congo, the Democratic Republic of the Congo, and Uganda), and the SDE has similarly shifted southwest-northeast (Figure 2).

This analysis showed clustered patterns in the distribution of DRMs across the world during the study period (2000–2017) (Figure 1). The results of other studies in Chennai (Chennai Corporation, Tamilnadu, India) (19) and rural areas of Bangladesh (12) also showed the clustered spatial pattern of DRMs. The results of the analysis showed that environmental factors such as contaminated water and food caused diarrhea and consequently led to mortality (20). Additionally, human factors such as social structures, lifestyles, race, culture, religion, immigration, and politics have also been factors contributing to DRMs, (21–25) which may have been the reason for the clustering of disease-related mortality worldwide. Cluster formation of disease-related mortality confirms that health issues always have spatial dimensions (26–30). Hence, it is recommended that health policymakers and planners study the causes of the formation of these hotspots.

The current study documents that Asian and African countries had the highest levels of DRM during the study period (2000–2017) (Figure 2). Diarrhea has been responsible for the deaths of more than 90% of children under five in low and lower-middle income countries. Regionally, South Asia and sub-Saharan Africa accounted for 88% of deaths in the same age group. The results of studies in India (11, 19) and Africa done at the local level in these countries are also similar to our study findings (31). These high levels of DRMs, as stated in other studies, are likely because of the socio-economic and cultural environments ensuing in the countries that have fewer resources and limited infrastructure to bear the disease burden (32, 33). Children living in deprived or isolated communities are particularly vulnerable to health hazards. In this regard, the result of the analysis showed that children died from preventable diseases because effective interventions were not provided equitably to all communities (1). Thus, children who are undernourished or have impaired immunity and people living with HIV have been most at risk of life-threatening diarrhea (4). Furthermore, variations in the impact of diarrhea among different communities might be due to diversity in awareness, attitude, and practices regarding diarrheal diseases. Besides, a feasible reason might also be due to environmental and infrastructural disparities such as access to water, availability and utilization of toilet facilities, access to hand washing facilities, and ways of waste disposal (34). Therefore, there is a need to increase the availability and accessibility of these facilities in targeted areas through a unified and comprehensive approach to reducing diarrhea-related morbidity and mortality among children under five (35). In some of the Asian and African counties that have the highest levels of DRM, due to poverty, undernutrition, poor hygiene, congested households with inadequate or no sanitation, and absence of proper care (10), children in these conditions are highly vulnerable to infections including diarrhea. In contrast, diarrhea-related mortality among children in developed countries has decreased in recent decades due to successful improvements in sanitation, hygiene, and access to antibiotics (9).

This study also found that DRM in children under five was prevalent in Asian countries until 2010 and has since shifted to African countries (Figure 2). The findings of our study confirm the theory of spatial distribution. According to the theory of spatial distribution, this relocation is probably influenced by environmental conditions and complex cultural and socio-economic processes (34, 35). However, this situation requires further investigation as emphasized by the WHO (4). Therefore, further research is recommended in this regard.

Our study indicated that GIS can be an effective tool for policymakers to identify changes in DRM worldwide. The results of other studies have also emphasized the efficacy of GIS to assess the risk of diarrhea in other regions (36, 37). GIS can be effective in understanding the distribution pathways, the trend of the disease spread, and their relationship to environmental factors (such as climatic conditions, water quality, health status, agricultural and industrial activities, and environmental contaminants), and assist in investigating the causes of diarrhea and its mortality. Moreover, the results from other studies reveal that a significant proportion of diarrheal diseases can be prevented through the provision of clean drinking water and adequate sanitation and hygiene (4). Therefore, we recommend GIS analysis for the effective and timely identification of DRM hotspots.

This research has mapped the incidence of DRM across the globe and generated fresh insights into the identification of DRM hotspots. The approach introduced in this paper can generate informed decision-making opportunities for policymakers and program planners. Besides, further spatial analysis of the identified hotspot areas by incorporating other factors such as health, environment, socioeconomic, and infrastructure could help health professionals to be prepared for the challenges ahead and develop customized intervention programs in the identified hotspots.

This study had several limitations. First, DRM could be affected by climatic factors such as rainfall, temperature, humidity, and so on, which we were unable to explore. Second, we could not examine the spatial pattern of DRM by gender. Third, we also did not have access to social variables and other lifestyle factors including socioeconomic status, drinking water supply, and toilet facilities that could have an impact on DRMs. Fourth, we only explored DRM globally and were unable to explore mortality from diarrhea in underdeveloped, developing, or developed/advanced countries separately.