Space-time Clustering Research Articles

Machine Learning-Based Multipath Components Clustering and Cluster Characteristics Analysis in High-Speed Railway Scenarios

Channel multipath components (MPCs) clustering and cluster characterization are the prerequisite for the development of cluster based channel models. This article investigates the MPCs clustering based on machine learning (ML) and analyzes the cluster characteristics in typical high-speed railway (HSR) scenarios. A variational Bayesian Gaussian mixture model (GMM)-based algorithm is introduced to achieve the space–time clustering of MPCs, which incorporates the statistical characteristics of MPCs and can automatically determine the optimum number of clusters. Moreover, a novel density-based validity index is proposed for evaluating the MPCs clustering performance. The proposed validity index improves the traditional index by considering the intracluster density, which can be calculated according to the Graham scanning method and Green’s formula. In addition to synthetic datasets, realistic MPCs datasets collected in an HSR obstructed viaduct scenario are used for the performance evaluation of the clustering algorithm and clustering validity index. Based on clustering results in the measured scenario, static cluster characteristics, including cluster number, intercluster and intracluster delay spreads (DSs) and angle spreads (ASs), and dynamic cluster characteristics such as cluster lifetime and birth and death property of clusters, are extracted and analyzed. These results will be useful for cluster-based channel modeling in future HSR mobile communication systems.

Public transportation network scan for rapid surveillance

As people move around using public transportation networks such as train and airplanes, it is expected that emerging infectious diseases will spread on the network. The scan statistics approach has been frequently applied to identify high-risk locations, and the results are widely used for making a clinical decision in a timely manner. However, they are not optimally designed for modeling the spread and might not effectively work in the emergency situation where computational time is essentially important. We propose a new scan statistics approach for the public transportation network, called PTNS (Public Transportation Network Scan). PTNS utilizes the available network structure to construct potential candidates of clusters, and thus it can work well especially in situations where public transportation is the main medium of the infection spread. Further, it is designed for rapid surveillance. Lastly, PTNS is generalized to detect space-time clusters by customizing the iteration for potential clusters creation. Using the simulation data generated with a real railway network, we showed that, PTNS outperformed the conventional methods, including Circular- and Flex-scan approaches, in terms of the detection performance, while the computational time is feasible.

A Non-Stationary 3D Model for 6G Massive MIMO mmWave UAV Channels

This paper proposes a non-stationary three-dimensional (3D) irregular-shaped geometry-based stochastic model (IS-GBSM) for fifth generation (5G) and beyond massive multiple-input multiple-output (MIMO) millimeter wave (mmWave) unmanned aerial vehicle (UAV) channels. This is the first sixth generation (6G) massive MIMO mmWave UAV IS-GBSM that can model the UAV channel space-time non-stationarity, and can describe the impact of some unique UAV-related parameters, e.g., the UAV’s moving direction, height, and speed, on channel statistical properties. To better represent the space-time non-stationarity in UAV scenarios, a novel UAV-related space-time cluster evolution algorithm is developed. The developed algorithm considers the characteristics of UAV communications on the modeling of space-time non-stationarity. Based on the proposed model, some channel statistical properties are derived and thoroughly investigated, including the space-time-frequency correlation function, Doppler power spectral density, envelope level crossing rate, and average fade duration. Some numerical results and interesting observations are given, and the impact of UAV-related parameters on channel statistical properties is explored, which can provide assistance for the design of 6G massive MIMO mmWave UAV communication systems. Finally, the applicability of the proposed model is verified by the close agreement between simulation results and measurement.

Clusters of malaria cases at sub-district level in endemic area in Java Island, Indonesia.

Malaria remains one of the essential public health problems in Indonesia. The year 2015 was originally set as the elimination target in Java Island, but there are still several regencies on Java reporting malaria cases. Spatial technology helps determine local variations in malaria transmission, control risk areas and assess the outcome of interventions. Information on distribution patterns of malaria at the sub-district level, presented as spatial, temporal, and spatiotemporal data, is vital in planning control interventions. Information on malaria transmission at the sub-district level in three regencies in Java (Banyumas, Kebumen, and Purbalingga) was collected from the Agency for Regional Development (Bappeda), the Population and Civil Registration Agency (Disdukcapil) and Statistics Indonesia (BPS). Global spatial autocorrelation and space-time clustering was investigated together with purely spatial and purely temporal analyses using geographical information systems (GIS) by ArcGis 10.2 and SaTScan 8.0 to detect areas at high risk of malaria. Our results show that malaria was spatially clustered in the study area in central Java, in particular in the Banyumas and Purbalingga regencies. The temporal analysis revealed that malaria clusters predominantly appeared in the period January-April. The results of the spatiotemporal analysis showed that there was one most likely malaria cluster and three secondary clusters in southern central Java. The most likely cluster was located in Purbalingga Regency covering one sub-district and remaining from the beginning of 2016 to the end of 2018. The approach used can assist the setting of resource priorities to control and eliminate malaria.

Public transportation network scan for rapid surveillance

As people move around using public transportation networks, such as train and airplanes, it is expected that emerging infectious diseases will spread on the network. The scan statistics approach has been frequently applied to identify high-risk locations, and the results are widely used for making a clinical decisions in a timely manner. However, they are not optimally designed for modeling the spread and might not effectively work under the emergency situation where computational time is essentially important. We propose a new scan statistics approach for the public transportation network, called PTNS (Public Transportation Network Scan). PTNS utilizes the available network structure to construct potential candidates of clusters, and thus it can work well especially in situations where public transportation is the main medium of the infection spread. Further, it is designed for rapid surveillance. Lastly, PTNS is generalized to detect space-time clusters by customizing the iteration for potential clusters creation. Using the simulation data generated with a real railway network, we showed that, PTNS outperformed the conventional methods, including Circular- and Flex-scan approaches in terms of the detection performance, while the computational time is feasible.

Detection of space-time clusters using a topological hierarchy for geospatial data on COVID-19 in Japan.

In this paper, we detected space–time clusters using data on coronavirus disease 2019 (COVID-19) collected daily by each prefecture in Japan. COVID-19 has spread globally since the first confirmed case in China, in December 2019. Several people have to date been infected in Japan since the first confirmed case in January 2020. The outbreak of COVID-19 has had a significant impact on many people’s lives. Studies are being conducted to detect regions, called clusters, which pose a significantly higher risk of infection than their surrounding areas, based on a spatial scan statistics of COVID-19 infections. Among these studies, space–time cluster detection has to date been actively performed to gain knowledge regarding infection status. Based on the spatial scan statistic, the cylindrical scan method is a widely used space–time cluster detection method. This method enables concurrent detection of the location and time of a cluster occurrence. However, this method cannot capture spatial changes in a cluster over time. When applying the existing method to a cluster whose shape changes over time, the number of calculations required becomes extremely large, and the analysis may become difficult. In this study, we focused on the hierarchical structure of the data obtained by conducting an echelon analysis and applied the space–time cluster detection method based on this structure to enable the capture of changes in a cluster’s shape. Furthermore, we visualized the location and period of a cluster’s occurrence and considered the cause of the cluster.

Space—Time Surveillance of COVID-19 Seasonal Clusters: A Case of Sweden

While COVID-19 is a global pandemic, different countries have experienced different morbidity and mortality patterns. We employ retrospective and prospective space–time permutation analysis on COVID-19 positive records across different municipalities in Sweden from March 2020 to February 2021, using data provided by the Swedish Public Health Agency. To the best of our knowledge, this is the first study analyzing nationwide COVID-19 space–time clustering in Sweden, on a season-to-season basis. Our results show that different municipalities within Sweden experienced varying extents of season-dependent COVID-19 clustering in both the spatial and temporal dimensions. The reasons for the observed differences could be related to the differences in the earlier exposures to the virus, the strictness of the social restrictions, testing capabilities and preparedness. By profiling COVID-19 space–time clusters before the introduction of vaccines, this study contributes to public health efforts aimed at containing the virus by providing plausible evidence in evaluating which epidemiologic interventions in the different regions could have worked and what could have not worked.

Space-Time Distribution Characteristics of Tuberculosis and Its Socioeconomic Factors in Southern China from 2015 to 2019.

PurposeGuangxi is a high prevalence area of tuberculosis (TB) in China, urgent needing of further TB reduction. Our purpose is to analyze the epidemiological characteristics of TB in Guangxi and analyze the relationship between socioeconomic factors and TB from the dimensions of time and space to provide evidence to effectively prevent and control TB.Patients and MethodsWe performed a retrospective analysis of the epidemiology of TB. Moran’s index (I) was used for spatial autocorrelation analysis, and space-time scanning was used to detect temporal, space, and space-time clusters of TB. A Bayesian space-time model was used to analyze related factors of the TB epidemic at the county level in Guangxi.ResultsFrom 2015 to 2019, a total of 233,623 TB cases were reported in Guangxi. The majority of TB cases were in males; the reported incidence of TB was the highest in people aged ≥65 years. By occupation, farmers were the most frequently affected. The overall reported incidence of TB decreased by 4.95% during this period. Tuberculosis occurs all year round, but the annual reporting peak is usually from March to July. Spatial autocorrelation analysis showed that the reported incidence of TB in 2015–2019 was spatially clustered (Moran’s I > 0, P < 0.05); Kulldorff’s scan revealed that the space-time cluster (log-likelihood ratio = 2683.76, relative risk = 1.60, P < 0.001) was mainly concentrated in northern Guangxi. Using Bayesian space-time modeling, socioeconomic and healthcare factors are related to the high prevalence of TB.ConclusionThe prevalence of TB is influenced by a space-time interaction effect and is associated with socioeconomic and healthcare status. It is necessary to improve the economic development and health service in areas with a high TB prevalence.

Spatial, temporal, and space-time clusters associated with opioid and cannabis poisoning events in U.S. dogs (2005-2014).

While a substantial amount of research has focused on the abuse of opioids and cannabinoids in human populations, few studies have investigated accidental poisoning events in pet populations. The objective of this study was to identify whether poisoning events involving opioids and cannabinoids clustered in space, time, and space-time, and compare the locations of clusters between the two toxicants. Data were obtained concerning reports of dog poisoning events from the American Society for the Prevention of Cruelty to Animals’ (ASPCA) Animal Poisoning Control Center (APCC), from 2005–2014. The spatial scan statistic was used to identify clusters with a high proportion of these poisoning events. Our analyses show that opioid and cannabinoid poisoning events clustered in space, time, and space-time. The cluster patterns identified for each toxicant were distinct, but both shared some similarities with human use data. This study may help increase awareness to the public, public health, and veterinary communities about where and when dogs were most affected by opioid and cannabinoid poisonings. This study highlights the need to educate dog owners about safeguarding opioid and cannabinoid products from vulnerable populations.

Detection of Space-Time Disease Clusters Using A Matrix Factorization Method

Space-time cluster detection has important applications in public health management and epidemiology to devise disease prevention strategies and to find the causes of a particular disease outbreak in a country. This study introduced a new method to detect the potential space-time clusters with no restriction on cluster shape and size and further visualize them distinctly on the heat map. The proposed algorithm is based on matrix factorization technique to find the significant components in spatial as well as temporal dimension. Applications to malaria data in Khyber Pakhtunkhwa, Pakistan shows that the proposed method is effective in detecting the potential clusters.

Spatiotemporal analysis of environmental and physiographic factors related to malaria in Bareilly district, India.

ObjectivesThe aim of this study was to explore the spatiotemporal clustering of reported malaria cases and to study the effects of various environmental and physiographic factors on malaria incidence in Bareilly district, Uttar Pradesh, India.Methods Malaria surveillance data were collected from the state health department and cleaned into an analyzable format. These data were analyzed along with meteorological, physiographic, and 2019 population data, which were obtained from the Indian Meteorological Department, National Aeronautics and Space Administration web portal, the Bhuvan platform of the Indian Space Research Organization, and the 2011 Census of India.ResultsIn total, 46,717 malaria cases were reported in Bareilly district in 2019, of which 25.99% were Plasmodium vivax cases and 74.01% were P. falciparum cases. The reported malaria cases in the district showed clustering, with significant spatial autocorrelation (Moran’s I value=0.63), and space-time clustering (p<0.01). A significant positive correlation was found between monthly malaria incidence and the monthly mean temperature (with a lag of 1−2 months) and rainfall (with a lag of 1 month). A significant negative correlation was detected between the elevation of blocks (i.e., intermediate-level administrative districts) and annual malaria reporting.Conclusion The presence of space-time clustering of malaria cases and its correlation with meteorological and physiographic factors indicate that routine spatial analysis of the surveillance data could help control and manage malaria outbreaks in the district.

Experimental study on fracture trace extension law of coal based on acoustic localization time–space cluster

Experimental study on fracture trace extension law of coal based on acoustic localization time–space cluster

Space-time risk cluster and time trends of congenital syphilis in Brazil: an ecological study.

Congenital syphilis (CS) is a problem of great concern for public health, especially in Brazil. The aim of this study was to analyse the time trends and the space-time dynamics of morbidity and mortality from CS in Brazil. An ecological and time series study, which included all cases and deaths from CS recorded in a national Brazilian database from 2013 to 2019 was performed. Time trends in CS incidence and mortality were assessed using segmented linear regression. Univariate global and local Moran indices and space-time scan statistics were used in the space and space-time analyses. A total of 183171 cases and 2401 deaths from CS were recorded in Brazil, with the highest number of cases being observed in the Southeast Region (n=82612 [45.1%]). Only 21.1% of pregnant mothers with syphilis received adequate treatment. There was an upward trend in CS rates among mothers ages 20-29y (average annual percent change [AAPC] 1.4 [95% confidence interval {CI} 1.0 to 1.7]) and with <8y of schooling (AAPC 6.6 [95% CI 5.3 to 7.9]). The primary space-time cluster involved 338 municipalities in the Southeast Region (relative risk 3.06, p<0.001) and occurred between 2017 and 2019. To reduce the trends in CS rates, it is necessary to develop actions to improve the quality of prenatal care and expand early diagnosis and adequate treatment of syphilis in pregnant women and their sexual partners, especially in groups with upward trends (mothers ages 20-29y and <8y of schooling) and living in higher-risk regions (Southeast, North and Northeast).

Targeting the search of African swine fever-infected wild boar carcasses: A tool for early detection.

This study analyses the temporal and spatial distribution of found dead African swine fever (ASF)-positive wild boar carcasses from 2017 to January 2021 in affected European countries: Bulgaria, Estonia, Germany, Hungary, Latvia, Lithuania, Romania, Poland, Serbia and Slovakia. During this period, a total of 21,785 cases were confirmed in 19,071 unique locations. The temporal analysis of aggregated cases per month evidenced that most countries located in southern latitudes showed a higher number of cases between January and April, whereas in northern latitudes there was no clear temporal pattern. The space-time K-function evidenced a space-time clustering in the ASF-positive wild boar carcasses, which was most prominent within distances of 2 km and within 1week. A Bayesian hierarchical spatial model was calibrated to evaluate the association between the probability of finding ASF-positive wild boar carcasses and landscape factors (i.e. the presence of a path and paved road), land use and wild boar abundance. Results showed the highest likelihood of finding ASF-positive wild boar carcasses in areas of transition between woodland and shrub, green urban areas and mixed forests. The presence of a path and a higher abundance of wild boar also increased slightly the odds of finding an ASF-positive dead wild boar. In summary, this paper aims to provide recommendations to design a search strategy to find ASF-infected wild boar carcasses, which is a crucial activity in the management of the disease, not just for surveillance purposes (i.e. the early detection of an introduction and the regular monitoring to understand the epidemiology and dynamics), but also for control, namely the disposal of infected carcasses as a virus source.

Prospective spatial-temporal clusters of COVID-19 in local communities: case study of Kansas City, Missouri, United States.

Kansas City, Missouri, became one of the major United States hotspots for COVID-19 due to an increase in the rate of positive COVID-19 test results. Despite the large numbers of positive cases in Kansas City, MO, the spatial-temporal analysis of data has been less investigated. However, it is critical to detect emerging clusters of COVID-19 and enforce control and preventive policies within those clusters. We conducted a prospective Poisson spatial-temporal analysis of Kansas City, MO data to detect significant space-time clusters of COVID-19 positive cases at the zip code level in Kansas City, MO. The analysis focused on daily infected cases in four equal periods of 3 months. We detected temporal patterns of emerging and re-emerging space-time clusters between March 2020 and February 2021. Three statistically significant clusters emerged in the first period, mainly concentrated in downtown. It increased to seven clusters in the second period, spreading across a broader region in downtown and north of Kansas City. In the third period, nine clusters covered large areas of north and downtown Kansas City, MO. Ten clusters were present in the last period, further extending the infection along the State Line Road. The statistical results were communicated with local health officials and provided the necessary guidance for decision-making and allocating resources (e.g., vaccines and testing sites). As more data become available, statistical clustering can be used as a COVID-19 surveillance tool to measure the effects of vaccination.

Detection of temporal, spatial and spatiotemporal clustering of malaria incidence in northwest Ethiopia, 2012\u20132020

Malaria is one of Ethiopia's most targeted communicable diseases for elimination. Malaria transmission varies significantly across space and time; and Ethiopia had space–time disparity in its transmission intensities. Considering heterogeneity and transmission intensity at the district level could play a crucial role in malaria prevention and elimination. This study aimed to explore temporal, spatial, and spatiotemporal clusters of malaria incidence in northwest Ethiopia. The analysis is based on monthly malaria surveillance data of districts and collected from the Amhara public health institute. The Kulldorff's retrospective space–time scan statistics using a discrete Poisson model were used to detect temporal, spatial, and space–time clusters of malaria incidence with and without adjusting the altitude + LLIN arm. Monthly malaria incidence had seasonal variations, and higher seasonal indices occurred in October and November. The temporal cluster occurred in the higher transmission season between September and December annually. The higher malaria incidence risk occurred between July 2012 and December 2013 (LLR = 414,013.41, RR = 2.54, P < 0.05). The purely spatial clustering result revealed that the most likely cluster occurred in the north and northwest parts of the region while secondary clusters varied in years. The space–time clusters were detected with and without considering altitude + LLIN arm. The most likely space–time cluster was concentrated in northwestern and western parts of the region with a high-risk period between July 2012 and December 2013 (LLR = 880,088.3, RR = 5.5, P < 0.001). We found eight significant space–time clusters using the altitude + LLIN arm. The most likely space–time cluster occurred in the western and northwestern parts of the region in July 2012–December 2013 (LLR = 886,097.7, RR = 5.55, P < 0.05). However, secondary clusters were located in eastern, northwestern, western parts of regions, which had different cases and relative risks in each cluster. Malaria transmission had temporal, spatial, and space–time variation in the region at the district level. Hence, considering these variations and factors contributing to malaria stratification would play an indispensable role in preventing and controlling practices that ultimately leads to malaria eliminations.

Evaluating the ability of a locally focused culling program in removing chronic wasting disease infected free-ranging white-tailed deer in Illinois, USA, 2003-2020.

In northern Illinois, chronic wasting disease (CWD) was first identified in free-ranging white-tailed deer (Odocoileus virginianus; hereafter referred to as "deer") in 2002. To reduce CWD transmission rates in Illinois, wildlife biologists have conducted locally focussed culling of deer since 2003 in areas where CWD has been detected. We used retrospective spatial, temporal and space-time scan statistical models to identify areas and periods where culling removed higher than expected numbers of CWD-positive deer. We included 490 Public Land Survey "sections" (∼2.59 km2 ) from 15 northern Illinois counties in which at least one deer tested positive for CWD between 2003 and 2020. A negative binomial regression model compared the proportion of CWD positive cases removed from sections with at least one CWD case detected in the previous years, "local area 1 (L1)," to the proportion of CWD cases in adjacent sections-L2, L3, and L4-designated by their increasing distance from L1. Of the 14,661 deer removed and tested via culling, 325 (2.22 %) were CWD-positive. A single temporal CWD cluster occurred in 2020. Three spatial clusters were identified, with a primary cluster located at the border of Boone and Winnebago counties. Four space-time clusters were identified with a primary cluster in the northern portion of the study area from 2003 to 2005 that overlapped with the spatial cluster. The proportion of CWD cases removed from L1 (3.92, 95% CI, 2.56-6.01) and L2 (2.32, 95% CI, 1.50-3.59) were significantly higher compared to L3. Focussing culling efforts on accessible properties closest to L1 areas results in more CWD-infected deer being removed, which highlights the value of collaborations among landowners, hunters, and wildlife management agencies to control CWD. Continuous evaluation and updating of the culling and surveillance programs are essential to mitigate the health burden of CWD on deer populations in Illinois.

Geographical distribution and space-time clustering of human illnesses with major Salmonella serotypes in Florida, USA, 2017-2018.

Nontyphoidal salmonellosis is the leading reported foodborne illness in Florida. Although the diversity of Salmonella serotypes circulating in Florida has been identified, the geographical characteristics of the major serotypes are poorly described. Here we examined the geospatial patterns of 803 whole-genome sequenced Salmonella isolates within seven major serotypes (Enteritidis, Newport, Javiana, Sandiego, Braenderup, Typhimurium and I 4,[5],12:i:-) with the metadata obtained from Florida Department of Health during 2017-2018. Geographically, the distribution of incidence rates varied distinctively between serotypes. Illnesses with Enteritidis and Newport serotypes were widespread in Florida. The incidence rate for Javiana was relatively higher in the north compared to the south. Typhimurium was concentrated in the northwest, while I 4,[5],12:i:-, the monophasic variant of Typhimurium was limited to the south. We also evaluated space-time clustering of isolates at the zip code level using scan statistic models. Space-time clusters were detected for each major serotype during 2017-2018. The multinomial scan statistic found the risk of illness with Javiana was higher in the north and southwest in the fall of 2017 compared to other major serotypes. This serotype-specific clustering analysis will assist in further unpacking the associations between distinct reservoirs and illnesses with major serotypes in Florida.

Spatio-Temporal Variation of Malaria Incidence and Risk Factors in West Gojjam Zone, Northwest Ethiopia.

Introduction:Malaria is a life-threatening acute febrile illness which is affecting the lives of millions globally. Its distribution is characterized by spatial, temporal, and spatiotemporal heterogeneity. Detection of the space-time distribution and mapping high-risk areas is useful to target hot spots for effective intervention.Methods:Time series cross sectional study was conducted using weekly malaria surveillance data obtained from Amhara Public Health Institute. Poisson model was fitted to determine the purely spatial, temporal, and space-time clusters using SaTScan™ 9.6 software. Spearman correlation, bivariate, and multivariable negative binomial regressions were used to analyze the relation of the climatic factors to count of malaria incidence.Result:Jabitenan, Quarit, Sekela, Bure, and Wonberma were high rate spatial cluster of malaria incidence hierarchically. Spatiotemporal clusters were detected. A temporal scan statistic identified 1 risk period from 1 July 2013 to 30 June 2015. The adjusted incidence rate ratio showed that monthly average temperature and monthly average rainfall were independent predictors for malaria incidence at all lag-months. Monthly average relative humidity was significant at 2 months lag.Conclusion:Malaria incidence had spatial, temporal, spatiotemporal variability in West Gojjam zone. Mean monthly temperature and rainfall were directly and negatively associated to count of malaria incidence respectively. Considering these space-time variations and risk factors (temperature and rainfall) would be useful for the prevention and control and ultimately achieve elimination.

Spatial and Space-time Clustering of Diarrhoeal Cases among Under-Five Children in Karkala, Karnataka: A Geospatial Analysis

Introduction: Globally, India tops by contributing the maximum number of diarrhoeal fatality. Forecasting the path and spread of diarrhoeal disease is critical due to its multifactorial cause, which needs robust spatial analysis and experiential investigations of communicable disease. Aim: To investigate purely spatial, purely temporal, and spacetime clusters of diarrhoea among under-five children using a Geographic Information System (GIS) in Karkala taluk of the Udupi district of Karnataka, India. Materials and Methods: A retrospective longitudinal study was conducted involving all the primary health centres of Karkala taluk by the investigators, from the Department of Public Health, K S Hegde Medical Academy, Nitte (DU), Mangalore, Karnataka, India. The data on diarrhoea among under-five children was collected for three years, i.e., from 1st April 2015 to 31st March 2018, at the Udupi district health office. A total of 49 village data were obtained, and 3894 under-five childhood diarrhoea were reported during the study period. The annual incidence of childhood diarrhoea at the taluk level was calculated using excel. The spatial, temporal and space-time diarrhoeal clusters were identified using Kulldorff SaTScan software. Geographic Information System, QGIS 3.20.2 software was used to plot the maps. Results: The analysis of the spatial cluster using SaTScan software for three years in the study area identified eight highrisk areas (p-value&lt;0.0001), covering 17 villages. The most likely spatiotemporal cluster region was located at the northern Karkala, and the most-at-risk period was 1st April 2016 to 30th September 2017 {Log Likelihood Ratio (LLR) =114.67 and p-value &lt;0.00001}. The analysis of purely temporal cluster showed that one most likely cluster happened in all villages (LLR= 73.89, p-value &lt;0.001) from 1st April 2017 to 3rd March 2018. Conclusion: The diarrhoea among under-five children at Karkala taluk was not randomly distributed over space and time.