Mapping the risk of respiratory infections using suburban district areas in a large city in Colombia.

BACKGROUND: Acute respiratory infections (ARI) in Cúcuta -Colombia, have a comparatively high burden of disease associated with high public health costs. However, little is known about the epidemiology of these diseases in the city and its distribution within suburban areas. This study addresses this gap by estimating and mapping the risk of ARI in Cúcuta and identifying the most relevant risk factors. METHODS: A spatial epidemiological analysis was designed to investigate the association of sociodemographic and environmental risk factors with the rate of ambulatory consultations of ARI in urban sections of Cúcuta, 2018. The ARI rate was calculated using a method for spatial estimation of disease rates. A Bayesian spatial model was implemented using the Integrated Nested Laplace Approximation approach and the Besag-York-Mollié specification. The risk of ARI per urban section and the hotspots of higher risk were also estimated and mapped. RESULTS: A higher risk of IRA was found in central, south, north and west areas of Cúcuta after adjusting for sociodemographic and environmental factors, and taking into consideration the spatial distribution of the city's urban sections. An increase of one unit in the percentage of population younger than 15 years; the Index of Multidimensional Poverty and the rate of ARI in the migrant population was associated with a 1.08 (1.06-1.1); 1.04 (1.01-1.08) and 1.25 (1.22-1.27) increase of the ARI rate, respectively. Twenty-four urban sections were identified as hotspots of risk in central, south, north and west areas in Cucuta. CONCLUSION: Sociodemographic factors and their spatial patterns are determinants of acute respiratory infections in Cúcuta. Bayesian spatial hierarchical models can be used to estimate and map the risk of these infections in suburban areas of large cities in Colombia. The methods of this study can be used globally to identify suburban areas and or specific communities at risk to support the implementation of prevention strategies and decision-making in the public and private health sectors.

Behavioral Strategies and the Spatial Pattern Formation of Nesting.

AbstractNesting in dense aggregations is common in central place foragers, such as group-living birds and insects. Both environmental heterogeneity and behavioral interactions are known to induce clustering of nests, but their relative importance remains unclear. We developed an individual-based model that simulated the spatial organization of nest building in a gregarious digger wasp, Bembix rostrata. This process-based model integrates environmental suitability, as derived from a microhabitat model, and relevant behavioral mechanisms related to local site fidelity and conspecific attraction. The drivers behind the nesting were determined by means of inverse modeling in which the emerging spatial and network patterns from simulations were compared with those observed in the field. Models with individual differences in behavior that include the simultaneous effect of a weak environmental cue and strong behavioral mechanisms yielded the best fit to the field data. The nest pattern formation of a central place foraging insect cannot be considered as the sum of environmental and behavioral mechanisms. We demonstrate the use of inverse modeling to understand complex processes that underlie nest aggregation in nature.

Bayesian spatio-temporal modelling and mapping of malaria and anaemia among children between 0 and 59 months in Nigeria.

BACKGROUND/M&M: A vital aspect of disease management and policy making lies in the understanding of the universal distribution of diseases. Nevertheless, due to differences all-over host groups and space-time outbreak activities, data are subject to intricacies. Herein, Bayesian spatio-temporal models were proposed to model and map malaria and anaemia risk ratio in space and time as well as to ascertain risk factors related to these diseases and the most endemic states in Nigeria. Parameter estimation was performed by employing the R-integrated nested Laplace approximation (INLA) package and Deviance Information Criteria were applied to select the best model. RESULTS: In malaria, model 7 which basically suggests that previous trend of an event cannot account for future trend i.e., Interaction with one random time effect (random walk) has the least deviance. On the other hand, model 6 assumes that previous event can be used to predict future event i.e., (Interaction with one random time effect (ar1)) gave the least deviance in anaemia. DISCUSSION: For malaria and anaemia, models 7 and 6 were selected to model and map these diseases in Nigeria, because these models have the capacity to receive strength from adjacent states, in a manner that neighbouring states have the same risk. Changes in risk and clustering with a high record of these diseases among states in Nigeria was observed. However, despite these changes, the total risk of malaria and anaemia for 2010 and 2015 was unaffected. CONCLUSION: Notwithstanding the methods applied, this study will be valuable to the advancement of a spatio-temporal approach for analyzing malaria and anaemia risk in Nigeria.

A Cortical Surface-Based Meta-Analysis of Human Reasoning.

Recent advances in neuroimaging have augmented numerous findings in the human reasoning process but have yielded varying results. One possibility for this inconsistency is that reasoning is such an intricate cognitive process, involving attention, memory, executive functions, symbolic processing, and fluid intelligence, whereby various brain regions are inevitably implicated in orchestrating the process. Therefore, researchers have used meta-analyses for a better understanding of neural mechanisms of reasoning. However, previous meta-analysis techniques include weaknesses such as an inadequate representation of the cortical surface's highly folded geometry. Accordingly, we developed a new meta-analysis method called Bayesian meta-analysis of the cortical surface (BMACS). BMACS offers a fast, accurate, and accessible inference of the spatial patterns of cognitive processes from peak brain activations across studies by applying spatial point processes to the cortical surface. Using BMACS, we found that the common pattern of activations from inductive and deductive reasoning was colocalized with the multiple-demand system, indicating that reasoning is a high-level convergence of complex cognitive processes. We hope surface-based meta-analysis will be facilitated by BMACS, bringing more profound knowledge of various cognitive processes.

Past, present, and future trends of overweight and obesity in Belgium using Bayesian age-period-cohort models.

BACKGROUND: Overweight and obesity are one of the most significant risk factors of the twenty-first century related to an increased risk in the occurrence of non-communicable diseases and associated increased healthcare costs. To estimate the future impact of overweight, the current study aimed to project the prevalence of overweight and obesity to the year 2030 in Belgium using a Bayesian age-period-cohort (APC) model, supporting policy planning. METHODS: Height and weight of 58,369 adults aged 18+ years, collected in six consecutive cross-sectional health interview surveys between 1997 and 2018, were evaluated. Criteria used for overweight and obesity were defined as body mass index (BMI) ≥ 25, and BMI ≥ 30. Past trends and projections were estimated with a Bayesian hierarchical APC model. RESULTS: The prevalence of overweight and obesity has increased between 1997 and 2018 in both men and women, whereby the highest prevalence was observed in the middle-aged group. It is likely that a further increase in the prevalence of obesity will be seen by 2030 with a probability of 84.1% for an increase in cases among men and 56.0% for an increase in cases among women. For overweight, it is likely to see an increase in cases in women (57.4%), while a steady state in cases among men is likely. A prevalence of 52.3% [21.2%; 83.2%] for overweight, and 27.6% [9.9%; 57.4%] for obesity will likely be achieved in 2030 among men. Among women, a prevalence of 49,1% [7,3%; 90,9%] for overweight, and 17,2% [2,5%; 61,8%] for obesity is most likely. CONCLUSIONS: Our projections show that the WHO target to halt obesity by 2025 will most likely not be achieved. There is an urgent necessity for policy makers to implement effective prevent policies and other strategies in people who are at risk for developing overweight and/or obesity.

Approximate Bayesian inference for case-crossover models.

A case-crossover analysis is used as a simple but powerful tool for estimating the effect of short-term environmental factors such as extreme temperatures or poor air quality on mortality. The environment on the day of each death is compared to the one or more "control days" in previous weeks, and higher levels of exposure on death days than control days provide evidence of an effect. Current state-of-the-art methodology and software (integrated nested Laplace approximation [INLA]) cannot be used to fit the most flexible case-crossover models to large datasets, because the likelihood for case-crossover models cannot be expressed in a manner compatible with this methodology. In this paper, we develop a flexible and scalable modeling framework for case-crossover models with linear and semiparametric effects which retains the flexibility and computational advantages of INLA. We apply our method to quantify nonlinear associations between mortality and extreme temperatures in India. An R package implementing our methods is publicly available.

Modeling Inoculum Availability of Plurivorosphaerella nawae in Persimmon Leaf Litter with Bayesian Beta Regression.

Circular leaf spot (CLS), caused by Plurivorosphaerella nawae, is a serious disease affecting persimmon (Diospyros kaki) that is characterized by necrotic lesions on leaves, defoliation, and fruit drop. Under Mediterranean conditions, P. nawae forms pseudothecia in the leaf litter in winter, and ascospores are released in spring, infecting susceptible leaves. Persimmon growers are advised to apply fungicides for CLS control during the period of inoculum availability, which was previously defined based on ascospore counts under the microscope. A model of inoculum availability of P. nawae was developed and evaluated as an alternative to ascospore counts. Leaf litter samples were collected weekly in L'Alcúdia (Spain) from 2010 to 2015. Leaves were soaked and placed in a wind tunnel, and the released ascospores of P. nawae were counted. Hierarchical Bayesian beta regression methods were used to model the dynamics of ascospore production in the leaf litter. The selected model included accumulated degree-days (ADDs) and ADDs taking into account the vapor pressure deficit (ADDvpd) as fixed effects and year as random effect. This model had a mean absolute error of 0.042 and a root mean square error of 0.062. The beta regression model was evaluated in four orchards from 2010 to 2015. Higher accuracy was obtained at the beginning and the end of the ascospore production period, which are the events of interest to schedule fungicide sprays for CLS control in Spain. This same modeling framework can be extended to other fungal plant pathogens whose inoculum dynamics are expressed as proportion data.[Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY 4.0 International license.

Estimating multilevel regional variation in excess mortality of cancer patients using integrated nested Laplace approximation.

Models of excess mortality with random effects were used to estimate regional variation in relative or net survival of cancer patients. Statistical inference for these models based on the Markov chain Monte Carlo (MCMC) methods is computationally intensive and, therefore, not feasible for routine analyses of cancer register data. This study assessed the performance of the integrated nested Laplace approximation (INLA) in monitoring regional variation in cancer survival. Poisson regression model of excess mortality including both spatially correlated and unstructured random effects was fitted to the data of patients diagnosed with ovarian and breast cancer in Finland during 1955-2014 with follow up from 1960 through 2014 by using the period approach with five-year calendar time windows. We estimated standard deviations associated with variation (i) between hospital districts and (ii) between municipalities within hospital districts. Posterior estimates based on the INLA approach were compared to those based on the MCMC simulation. The estimates of the variation parameters were similar between the two approaches. Variation within hospital districts dominated in the total variation between municipalities. In 2000-2014, the proportion of the average variation within hospital districts was 68% (95% posterior interval: 35%-93%) and 82% (60%-98%) out of the total variation in ovarian and breast cancer, respectively. In the estimation of regional variation, the INLA approach was accurate, fast, and easy to implement by using the R-INLA package.

A spatiotemporal back-calculation approach to estimate cancer incidence measures.

Incidence rates are an important population-level disease risk measure. Cancer incidence data in the United States, which are collected by disease registries, have been spatiotemporally sparse. Back-calculation methods can yield incidence estimates for a spatial domain by solving a convolution equation that relates mortality to incidence through survival estimates. We propose a novel back-calculation approach that uses spatiotemporal age-period-cohort (APC) modeling to estimate incidence for spatial units within a region. The method is applied to state-specific lung cancer data in the United States for males ages 30 to 84 in years 1975-2004. SEER data are used to model cancer progression from incidence to mortality along three timescales (APC) and across four regions. Using mortality data from National Vital Statistics System, incidence is back-calculated for unique birth cohorts in 49 states. A conditionally autoregressive model with cubic splines for temporal effects is used to smooth back-calculated estimates. Bayesian estimates of model parameters are obtained using integrated nested Laplace approximation. Results show varying time trends in lung cancer risk across states, which may quantify effects of state policies.

Bayesian bivariate meta-analysis of diagnostic test studies with interpretable priors.

In a bivariate meta-analysis, the number of diagnostic studies involved is often very low so that frequentist methods may result in problems. Using Bayesian inference is particularly attractive as informative priors that add a small amount of information can stabilise the analysis without overwhelming the data. However, Bayesian analysis is often computationally demanding and the selection of the prior for the covariance matrix of the bivariate structure is crucial with little data. The integrated nested Laplace approximations method provides an efficient solution to the computational issues by avoiding any sampling, but the important question of priors remain. We explore the penalised complexity (PC) prior framework for specifying informative priors for the variance parameters and the correlation parameter. PC priors facilitate model interpretation and hyperparameter specification as expert knowledge can be incorporated intuitively. We conduct a simulation study to compare the properties and behaviour of differently defined PC priors to currently used priors in the field. The simulation study shows that the PC prior seems beneficial for the variance parameters. The use of PC priors for the correlation parameter results in more precise estimates when specified in a sensible neighbourhood around the truth. To investigate the usage of PC priors in practice, we reanalyse a meta-analysis using the telomerase marker for the diagnosis of bladder cancer and compare the results with those obtained by other commonly used modelling approaches. Copyright © 2017 John Wiley & Sons, Ltd.

A methodological framework for the improved use of routine health system data to evaluate national malaria control programs: evidence from Zambia.

BACKGROUND: Due to challenges in laboratory confirmation, reporting completeness, timeliness, and health access, routine incidence data from health management information systems (HMIS) have rarely been used for the rigorous evaluation of malaria control program scale-up in Africa. METHODS: We used data from the Zambia HMIS for 2009-2011, a period of rapid diagnostic and reporting scale-up, to evaluate the association between insecticide-treated net (ITN) program intensity and district-level monthly confirmed outpatient malaria incidence using a dose-response national platform approach with district-time units as the unit of analysis. A Bayesian geostatistical model was employed to estimate longitudinal district-level ITN coverage from household survey and programmatic data, and a conditional autoregressive model (CAR) was used to impute missing HMIS data. The association between confirmed malaria case incidence and ITN program intensity was modeled while controlling for known confounding factors, including climate variability, reporting, testing, treatment-seeking, and access to health care, and additionally accounting for spatial and temporal autocorrelation. RESULTS: An increase in district level ITN coverage of one ITN per household was associated with an estimated 27% reduction in confirmed case incidence overall (incidence rate ratio (IRR): 0 · 73, 95% Bayesian Credible Interval (BCI): 0 · 65-0 · 81), and a 41% reduction in areas of lower malaria burden. CONCLUSIONS: When improved through comprehensive parasitologically confirmed case reporting, HMIS data can become a valuable tool for evaluating malaria program scale-up. Using this approach we provide further evidence that increased ITN coverage is associated with decreased malaria morbidity and use of health services for malaria illness in Zambia. These methods and results are broadly relevant for malaria program evaluations currently ongoing in sub-Saharan Africa, especially as routine confirmed case data improve.

The hospitalisation risk of chronic circulatory and respiratory diseases associated with coal mining in the general population in Queensland, Australia.

Queensland is the main coal mining state in Australia where populations in coal mining areas have been historically exposed to coal mining emissions. Although a higher risk of chronic circulatory and respiratory diseases has been associated with coal mining globally, few studies have investigated these associations in the Queensland general population. This study estimates the association of coal production with hospitalisations for chronic circulatory and respiratory diseases in Queensland considering spatial and temporal variations during 1997-2014. An ecological analysis used a Bayesian hierarchical spatiotemporal model to estimate the association of coal production with standardised rates of each, chronic circulatory and respiratory diseases, adjusting for sociodemographic factors and considering the spatial structure of Queensland's statistical areas (SA2) in the 18-year period. Two specifications; with and without a space-time interaction effect were compared using the integrated nested Laplace approximation -INLA approach. The posterior mean of the best fit model was used to map the spatial, temporal and spatiotemporal trends of risk. The analysis considered 2,831,121 hospitalisation records. Coal mining was associated with a 4 % (2.4-5.5) higher risk of hospitalisation for chronic respiratory diseases in the model with a space-time interaction effect which had the best fit. An emerging higher risk of either chronic circulatory and respiratory diseases was identified in eastern areas and some coal-mining areas in central and southeast Queensland. There were important disparities in the spatiotemporal trend of risk between coal -and non-coal mining areas for each, chronic circulatory and respiratory diseases. Coal mining is associated with an increased risk of chronic respiratory diseases in the Queensland general population. Bayesian spatiotemporal analyses are robust methods to identify environmental determinants of morbidity in exposed populations. This methodology helps identifying at-risk populations which can be useful to support decision-making in health. Future research is required to investigate the causality links between coal mining and these diseases.

Spatiotemporal hierarchical Bayesian analysis to identify factors associated with COVID-19 in suburban areas in Colombia.

Introduction: The pandemic had a profound impact on the provision of health services in Cúcuta, Colombia where the neighbourhood-level risk of Covid-19 has not been investigated. Identifying the sociodemographic and environmental risk factors of Covid-19 in large cities is key to better estimate its morbidity risk and support health strategies targeting specific suburban areas. This study aims to identify the risk factors associated with the risk of Covid-19 in Cúcuta considering inter -spatial and temporal variations of the disease in the city's neighbourhoods between 2020 and 2022. Methods: Age-adjusted rate of Covid-19 were calculated in each Cúcuta neighbourhood and each quarter between 2020 and 2022. A hierarchical spatial Bayesian model was used to estimate the risk of Covid-19 adjusting for socioenvironmental factors per neighbourhood across the study period. Two spatiotemporal specifications were compared (a nonparametric temporal trend; with and without space-time interaction). The posterior mean of the spatial and spatiotemporal effects was used to map the Covid-19 risk. Results: There were 65,949 Covid-19 cases in the study period with a varying standardized Covid-19 rate that peaked in October-December 2020 and April-June 2021. Both models identified an association of the poverty and stringency indexes, education level and PM10 with Covid-19 although the best fit model with a space-time interaction estimated a strong association with the number of high-traffic roads only. The highest risk of Covid-19 was found in neighbourhoods in west, central, and east Cúcuta. Conclusions: The number of high-traffic roads is the most important risk factor of Covid-19 infection in Cucuta. This indicator of mobility and connectivity overrules other socioenvironmental factors when Bayesian models include a space-time interaction. Bayesian spatial models are important tools to identify significant determinants of Covid-19 and identifying at-risk neighbourhoods in large cities. Further research is needed to establish causal links between these factors and Covid-19.

Spatiotemporal Variation and Predictors of Unsuppressed Viral Load among HIV-Positive Men and Women in Rural and Peri-Urban KwaZulu-Natal, South Africa.

Unsuppressed HIV viral load is an important marker of sustained HIV transmission. We investigated the prevalence, predictors, and high-risk areas of unsuppressed HIV viral load among HIV-positive men and women. Unsuppressed HIV viral load was defined as viral load of ≥400 copies/mL. Data from the HIV Incidence District Surveillance System (HIPSS), a longitudinal study undertaken between June 2014 to June 2016 among men and women aged 15−49 years in rural and peri-urban KwaZulu-Natal, South Africa, were analysed. A Bayesian geoadditive regression model which includes a spatial effect for a small enumeration area was applied using an integrated nested Laplace approximation (INLA) function while accounting for unobserved factors, non-linear effects of selected continuous variables, and spatial autocorrelation. The prevalence of unsuppressed HIV viral load was 46.1% [95% CI: 44.3−47.8]. Predictors of unsuppressed HIV viral load were incomplete high school education, being away from home for more than a month, alcohol consumption, no prior knowledge of HIV status, not ever tested for HIV, not on antiretroviral therapy (ART), on tuberculosis (TB) medication, having two or more sexual partners in the last 12 months, and having a CD4 cell count of <350 cells/µL. A positive non-linear effect of age, household size, and the number of lifetime HIV tests was identified. The higher-risk pattern of unsuppressed HIV viral load occurred in the northwest and northeast of the study area. Identifying predictors of unsuppressed viral load in a localized geographic area and information from spatial risk maps are important for targeted prevention and treatment programs to reduce the transmission of HIV.

The association of wildfire air pollution with COVID-19 incidence in New South Wales, Australia.

The 2020 COVID-19 outbreak in New South Wales (NSW), Australia, followed an unprecedented wildfire season that exposed large populations to wildfire smoke. Wildfires release particulate matter (PM), toxic gases and organic and non-organic chemicals that may be associated with increased incidence of COVID-19. This study estimated the association of wildfire smoke exposure with the incidence of COVID-19 in NSW. A Bayesian mixed-effect regression was used to estimate the association of either the average PM10 level or the proportion of wildfire burned area as proxies of wildfire smoke exposure with COVID-19 incidence in NSW, adjusting for sociodemographic risk factors. The analysis followed an ecological design using the 129 NSW Local Government Areas (LGA) as the ecological units. A random effects model and a model including the LGA spatial distribution (spatial model) were compared. A higher proportional wildfire burned area was associated with higher COVID-19 incidence in both the random effects and spatial models after adjustment for sociodemographic factors (posterior mean = 1.32 (99% credible interval: 1.05-1.67) and 1.31 (99% credible interval: 1.03-1.65), respectively). No evidence of an association between the average PM10 level and the COVID-19 incidence was found. LGAs in the greater Sydney and Hunter regions had the highest increase in the risk of COVID-19. This study identified wildfire smoke exposures were associated with increased risk of COVID-19 in NSW. Research on individual responses to specific wildfire airborne particles and pollutants needs to be conducted to further identify the causal links between SARS-Cov-2 infection and wildfire smoke. The identification of LGAs with the highest risk of COVID-19 associated with wildfire smoke exposure can be useful for public health prevention and or mitigation strategies.

Mapping the Morbidity Risk Associated with Coal Mining in Queensland, Australia.

The populations in the vicinity of surface coal mining activities have a higher risk of morbidity due to diseases, such as cardiovascular, respiratory and hypertensive diseases, as well as cancer and diabetes mellitus. Despite the large and historical volume of coal production in Queensland, the main Australian coal mining state, there is little research on the association of coal mining exposures with morbidity in non-occupational populations in this region. This study explored the association of coal production (Gross Raw Output-GRO) with hospitalisations due to six disease groups in Queensland using a Bayesian spatial hierarchical analysis and considering the spatial distribution of the Local Government Areas (LGAs). There is a positive association of GRO with hospitalisations due to circulatory diseases (1.022, 99% CI: 1.002-1.043) and respiratory diseases (1.031, 95% CI: 1.001-1.062) for the whole of Queensland. A higher risk of circulatory, respiratory and chronic lower respiratory diseases is found in LGAs in northwest and central Queensland; and a higher risk of hypertensive diseases, diabetes mellitus and lung cancer is found in LGAs in north, west, and north and southeast Queensland, respectively. These findings can be used to support public health strategies to protect communities at risk. Further research is needed to identify the causal links between coal mining and morbidity in non-occupational populations in Queensland.

Spatiotemporal modeling of ecological and sociological predictors of West Nile virus in Suffolk County, NY, mosquitoes.

Suffolk County, New York, is a locus for West Nile virus (WNV) infection in the American northeast that includes the majority of Long Island to the east of New York City. The county has a system of light and gravid traps used for mosquito collection and disease monitoring. In order to identify predictors of WNV incidence in mosquitoes and predict future occurrence of WNV, we have developed a spatiotemporal Bayesian model, beginning with over 40 ecological, meteorological, and built-environment covariates. A mixed-effects model including spatially and temporally correlated errors was fit to WNV surveillance data from 2008 to 2014 using the R package "R-INLA," which allows for Bayesian modeling using the stochastic partial differential equation (SPDE) approach. The integrated nested Laplace approximation (INLA) SPDE allows for simultaneous fitting of a temporal parameter and a spatial covariance, while incorporating a variety of likelihood functions and running in R statistical software on a home computer. We found that land cover classified as open water and woody wetlands had a negative association with WNV incidence in mosquitoes, and the count of septic systems was associated with an increase in WNV. Mean temperature at two-week lag was associated with a strong positive impact, while mean precipitation at no lag and one-week lag was associated with positive and negative impacts on WNV, respectively. Incorporation of spatiotemporal factors resulted in a marked increase in model goodness-of-fit. The predictive power of the model was evaluated on 2015 surveillance results, where the best model achieved a sensitivity of 80.9% and a specificity of 77.0%. The spatial covariate was mapped across the county, identifying a gradient of WNV prevalence increasing from east to west. The Bayesian spatiotemporal model improves upon previous approaches, and we recommend the INLA SPDE methodology as an efficient way to develop robust models from surveillance data to develop and enhance monitoring and control programs. Our study confirms previously found associations between weather conditions and WNV and suggests that wetland cover has a mitigating effect on WNV infection in mosquitoes, while high septic system density is associated with an increase in WNV infection.

Spatial and Spatio-Temporal Models for Modeling Epidemiological Data with Excess Zeros.

Epidemiological data often include excess zeros. This is particularly the case for data on rare conditions, diseases that are not common in specific areas or specific time periods, and conditions and diseases that are hard to detect or on the rise. In this paper, we provide a review of methods for modeling data with excess zeros with focus on count data, namely hurdle and zero-inflated models, and discuss extensions of these models to data with spatial and spatio-temporal dependence structures. We consider a Bayesian hierarchical framework to implement spatial and spatio-temporal models for data with excess zeros. We further review current implementation methods and computational tools. Finally, we provide a case study on five-year counts of confirmed cases of Lyme disease in Illinois at the county level.