Hierarchical Bayesian Approach Research Articles

The Effect of Loan Debt on Graduation by Department: a Bayesian Hierarchical Approach

Using data from three cohorts at the University of Delaware, this study investigates the effects of student loan debt on six-year graduation by department over five years. The effects are estimated from five Bayesian hierarchical models, one model for each year. The Bayesian hierarchical model uses a partial pooling technique to address the over-fitting issue when estimating the effects of loan debt, and this technique is especially beneficial to departments with small enrollments. Similar to the observation that financial aid has different effects by racial and ethnic groups, and socioeconomic groups, findings suggest a pronounced department-level loan debt effect for first-year students that diminishes as students progress through their academic career. These findings suggest that a strategy that considers a students’ academic department when designing a financial aid policy would optimize the efficiency of institutional financial resources. Moreover, universities exploring differential financial aid policies by department should start with randomized trials using first-year students.

Modelling supply chain disruption analytics under insufficient data: A decision support system based on Bayesian hierarchical approach

Recent disruptions in global and local supply chains (SCs) due to manmade and natural disasters have drawn a lot of attention to academics and practitioners. Such disruptions are often characterized by a lack of insufficient data. To tackle such a data scarce supply chain ecosystem, this article examines the potential disruption risks in SCs under insufficient input data. For this, a decision support system (DSS) based on the Bayesian hierarchical approach and value at risk (VaR) reduction analysis is proposed to assess a supplier's disruption risk events probability as well as the supplier revenue impact on a company of interest. Empirical data are used to examine the DSS. The findings show that the DSS is effective in generating the suppliers’ risk profiles. The proposed DSS can be utilized by supply chain managers and practitioners to manage SC disruption risks in a more efficient manner.

Forecasted 2040 global prevalence of nonalcoholic fatty liver disease using hierarchical bayesian approach.

Due to increases in obesity and type 2 diabetes, the prevalence of nonalcoholic fatty liver disease (NAFLD) has also been increasing. Current forecast models may not include non-obese NAFLD. Here, we used the Bayesian approach to forecast the prevalence of NAFLD through the year 2040. Prevalence data from 245 articles involving 2,699,627 persons were used with a hierarchical Bayesian approach to forecast the prevalence of NAFLD through 2040. Subgroup analyses were performed for age, gender, presence of metabolic syndrome, region, and smoking status. Sensitivity analysis was conducted for clinical setting and study quality. The forecasted 2040 prevalence was 55.7%, a three-fold increase since 1990 and a 43.2% increase from the 2020 prevalence of 38.9%. The estimated average yearly increase since 2020 was 2.16%. For those aged <50 years and ≥50 years, the 2040 prevalence were not significantly different (56.7% vs. 61.5%, P=0.52). There was a significant difference in 2040 prevalence by sex (males: 60% vs. 50%) but the trend was steeper for females (annual percentage change: 2.5% vs. 1.5%, P=0.025). There was no difference in trends overtime by region (P=0.48). The increase rate was significantly higher in those without metabolic syndrome (3.8% vs. 0.84%, P=0.003) and smokers (1.4% vs. 1.1%, P=0.011). There was no difference by clinical/community setting (P=0.491) or study quality (P=0.85). By 2040, over half the adult population is forecasted to have NAFLD. The largest increases are expected to occur in women, smokers, and those without metabolic syndrome. Intensified efforts are needed to raise awareness of NAFLD and to determine long-term solutions addressing the driving factors of the disease.

How Neighborhood Characteristics Influence Neighborhood Crimes: A Bayesian Hierarchical Spatial Analysis.

Urban crimes are a severe threat to livable and sustainable urban environments. Many studies have investigated the patterns, causes, and strategies for curbing the occurrence of urban crimes. It is found that neighborhood socioeconomic status, physical environment, and ethnic composition all might play a role in the occurrence of urban crimes. Inspired by the recent interest in exploring urban crime patterns with spatial data analysis techniques and the development of Bayesian hierarchical analytical approaches, we attempt to explore the inherently intricate relationships between urban assaultive violent crimes and the neighborhood socioeconomic status, physical environment, and ethnic composition in Paterson, NJ, using census data of the American Community Survey, alcohol and tobacco sales outlet data, and abandoned property listing data from 2013. Analyses are set at the census block group level. Urban crime data are obtained from the Paterson Police Department. Instead of examining relationships at a global level with both non-spatial and spatial analyses, we examine in depth the potential locally varying relationships at the local level through a Bayesian hierarchical spatially varying coefficient model. At both the global and local analysis levels, it is found that median household income is decisively negatively related to urban crime occurrence. Percentage of African Americans and Hispanics, number of tobacco sales outlets, and number of abandoned properties are all positively related with urban crimes. At the local level of analysis, however, the different factors have varying influence on crime occurrence throughout the city of Paterson, with median household income having the broadest influence across the city. The practice of applying a Bayesian hierarchical spatial analysis framework to understand urban crime occurrence and urban neighborhood characteristics enables urban planners, stakeholders, and public safety officials to engage in more active and targeted crime-reduction strategies.

Divergent Effects of Factors on Crash Severity under Autonomous and Conventional Driving Modes Using a Hierarchical Bayesian Approach.

Influencing factors on crash severity involved with autonomous vehicles (AVs) have been paid increasing attention. However, there is a lack of comparative analyses of those factors between AVs and human-driven vehicles. To fill this research gap, the study aims to explore the divergent effects of factors on crash severity under autonomous and conventional (i.e., human-driven) driving modes. This study obtained 180 publicly available autonomous vehicle crash data, and 39 explanatory variables were extracted from three categories, including environment, roads, and vehicles. Then, a hierarchical Bayesian approach was applied to analyze the impacting factors on crash severity (i.e., injury or no injury) under both driving modes with considering unobserved heterogeneities. The results showed that some influencing factors affected both driving modes, but their degrees were different. For example, daily visitors’ flowrate had a greater impact on the crash severity under the conventional driving mode. More influencing factors only had significant impacts on one of the driving modes. For example, in the autonomous driving mode, mixed land use increased the severity of crashes, while daytime had the opposite effects. This study could contribute to specifying more appropriate policies to reduce the crash severity of both autonomous and human-driven vehicles especially in mixed traffic conditions.

Multi-Platform LiDAR for Non-Destructive Individual Aboveground Biomass Estimation for Changbai Larch (Larix olgensis Henry) Using a Hierarchical Bayesian Approach

Individual-tree aboveground biomass (AGB) estimation is vital for precision forestry and still worth exploring using multi-platform LiDAR data for high accuracy and efficiency. Based on the unmanned aerial vehicle and terrestrial LiDAR data, this study explores the feasibility of the individual tree AGB estimation of Changbai larch (Larix olgensis Henry) of eight plots from three different regions in Maoershan Forest Farm of Heilongjiang, China, using nonlinear mixed effect model with hierarchical Bayesian approach. Results showed that the fused LiDAR data estimated the individual tree parameters (i.e., diameter at breast height (DBH), tree height (TH), and crown projection area (CPA)) with high accuracies (all R2 &gt; 0.9 and relatively low RMSE and rRMSE) using region-based hierarchical cross-section analysis (RHCSA) algorithm. Considering regions as random variables, the nonlinear mixed-effects AGB model with three predictor variables (i.e., DBH, TH, and CPA) performed better than its corresponding nonlinear model. In addition, the hierarchical Bayesian method provided better model-fitting performances and more stable parameter estimates than the classical method (i.e., nonlinear mixed-effect model), especially for small sample sizes (e.g., &lt;50). This methodology (i.e., multi-platform LiDAR data and the hierarchical Bayesian method) provides a potential solution for non-destructive individual-tree AGB modeling with small sample size and high accuracy in both forestry and remote sensing communities.

Examining Seat Belt Use Habits in Wyoming: A Bayesian Hierarchical Logit Approach

Wyoming has one of the lowest seat belt law compliance rates in the United States. Understanding the factors associated with seat belt non-use is crucial for the development of appropriate mitigation measures that aid in increasing seat belt usage rates. In this study, Bayesian binary logistic regression models were developed to: i) investigate the factors associated with daytime seat belt non-use using observational survey data; and ii) assess the factors related to seat belt non-use in fatal crashes while accounting for possible intra-class correlation (effects of unobserved factors common to occupants in the same vehicle). The results indicated that males were less likely to use seat belts than females. Also, trips made in pick-up trucks, those made within urban areas, those made during weekdays, and those made by means of vehicles with Wyoming license plates were likely to involve seat belt non-use. Furthermore, counties with thriving oil and gas industries had lower seat belt use rates. It was also inferred that young occupants, rear seat occupants, impairment, weekdays, traveling around midnight, traveling on collector roads, and traveling on local roads were associated with seat belt non-use. A strong correlation in seat belt non-use among occupants within the same vehicle warrants the implementation of the hierarchical logistic model to investigate seat belt use among occupants involved in fatal crashes. The findings of this study highlight remarkable trends in seat belt use habits in Wyoming, which will aid legislatures in proposing road safety measures aimed at raising seat belt usage proportions.

Random-Parameter Bayesian Hierarchical Extreme Value Modeling Approach with Heterogeneity in Means and Variances for Traffic Conflict–Based Crash Estimation

Random-Parameter Bayesian Hierarchical Extreme Value Modeling Approach with Heterogeneity in Means and Variances for Traffic Conflict–Based Crash Estimation

A dynamic hierarchical Bayesian approach for forecasting vegetation condition

Abstract. Agricultural drought, which occurs due to a significant reduction in the moisture required for vegetation growth, is the most complex amongst all drought categories. The onset of agriculture drought is slow and can occur over vast areas with varying spatial effects, differing in areas with a particular vegetation land cover or specific agro-ecological sub-regions. These spatial variations imply that monitoring and forecasting agricultural drought require complex models that consider the spatial variations in a given region of interest. Hierarchical Bayesian models are suited for modelling such complex systems. Using partially pooled data with sub-groups that characterise spatial differences, these models can capture the sub-group variation while allowing flexibility and information sharing between these sub-groups. This paper's objective is to improve the accuracy and precision of agricultural drought forecasting in spatially diverse regions with a hierarchical Bayesian model. Results showed that the hierarchical Bayesian model was better at capturing the variability for the different agro-ecological zones and vegetation land covers compared to a regular Bayesian auto-regression distributed lags model. The forecasted vegetation condition and associated drought probabilities were more accurate and precise with the hierarchical Bayesian model at 4- to 10-week lead times. Forecasts from the hierarchical model exhibited higher hit rates with a low probability of false alarms for drought events in semi-arid and arid zones. The hierarchical Bayesian model also showed good transferable forecast skills over counties not included in the training data.

Hierarchical Bayesian modeling for knowledge transfer across engineering fleets via multitask learning

AbstractA population‐level analysis is proposed to address data sparsity when building predictive models for engineering infrastructure. Utilizing an interpretable hierarchical Bayesian approach and operational fleet data, domain expertise is naturally encoded (and appropriately shared) between different subgroups, representing (1) use‐type, (2) component, or (3) operating condition. Specifically, domain expertise is exploited to constrain the model via assumptions (and prior distributions) allowing the methodology to automatically share information between similar assets, improving the survival analysis of a truck fleet (15% and 13% increases in predictive log‐likelihood of hazard) and power prediction in a wind farm (up to 82% reduction in the standard deviation of maximum output prediction). In each asset management example, a set of correlated functions is learnt over the fleet, in a combined inference, to learn a population model. Parameter estimation is improved when subfleets are allowed to share correlated information at different levels in the hierarchy; the (averaged) reduction in standard deviation for interpretable parameters in the survival analysis is 70%, alongside 32% in wind farm power models. In turn, groups with incomplete data automatically borrow statistical strength from those that are data‐rich. The statistical correlations enable knowledge transfer via Bayesian transfer learning, and the correlations can be inspected to inform which assets share information for which effect (i.e., parameter). Successes in both case studies demonstrate the wide applicability in practical infrastructure monitoring, since the approach is naturally adapted between interpretable fleet models of different in situ examples.

Obesity and labour market outcomes in Italy: a dynamic panel data evidence with correlated random effects.

This paper investigates the effects of obesity, socio-economic variables, and individual-specific factors on work productivity across Italian regions. A dynamic panel data with correlated random effects is used to jointly deal with incidental parameters, endogeneity issues, and functional forms of misspecification. Methodologically, a hierarchical semiparametric Bayesian approach is involved in shrinking high dimensional model classes, and then obtaining a subset of potential predictors affecting outcomes. Monte Carlo designs are addressed to construct exact posterior distributions and then perform accurate forecasts. Cross-sectional Heterogeneity is modelled nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-specific regressors. Prevention policies and strategies to handle health and labour market prospects are also discussed.

A hierarchical Constrained Bayesian (ConBay) approach to jointly estimate water storage and Post-Glacial Rebound from GRACE(-FO) and GNSS data

A hierarchical Constrained Bayesian (ConBay) approach to jointly estimate water storage and Post-Glacial Rebound from GRACE(-FO) and GNSS data

Evidence of parameters underestimation from nonlinear growth models for data classified as limited

Some growth data in aquaculture have peculiar characteristics that generate consequences in the analysis and modeling. They are usually incomplete or limited, as classified in this article. This means data are restricted to a few observations and often are limited to observations below the curve’s inflection point due to economic interests in farm settings, or due to limitation of physical space in controlled research laboratories, for example. This possibly causes under and/or overestimation in the inference of nonlinear models. Through shrimp growth simulations from the Michaelis–Menten curve, the limited data were synthesized with threshold observation up to the first 7, 13, 18, 36, and 82 weeks. Seven sigmoid growth functions (Logistic, Gompertz, von Bertalanffy, Richard, Weibull, Morgan–Mercer–Flodin, and the own Michaelis–Menten growth) were fitted to respective limited data, in order to assess the research hypothesis. Taking the scenarios with incompleteness in the first 7, 13 and 18 weeks, the parameters of all growth curves modeled under a frequentist approach were underestimated. Thus, we propose a correction for this possible problem through a hierarchical Bayesian approach. Real data from shrimp farming in northeastern Brazil were used to compare it with the traditional frequentist approach employed. The sensitivity in detecting outstanding treatment (pond or batch level hierarchy) can make the new method a powerful management tool in animal production, and also in trials designed for scientific research.

Sedimentation supports life-cycle CH4 production and accumulation in a river valley reservoir: A hierarchical Bayesian modeling approach

Reservoirs have been recognized as a source of methane (CH4). With the gradual increase in the number of the world's reservoirs, predicting the long-term variation of reservoir CH4 emissions is important to understand the global change in carbon cycling due to reservoir creation and operation. Here, we first categorized the origins and transport of organic carbon (OC) by reservoir creation and operation into the following four aspects: a) the decomposition of flooded organic matter, b) the sedimentation of OC from upstream sediment inputs, c) the transition of the aquatic ecosystem from lotic to lentic type, stimulating the production of autochthonous OC; and d) reservoir as the collector of anthropogenic OC inputs from surrounding communities. It was assumed that OC from the four aspects jointly determined the production and accumulation of reservoir CH4 concentration, supporting life-cycle reservoir CH4 emissions. A hierarchical Bayesian model of reservoir CH4 concentration was established and calibrated by observed monthly datasets in 2018 in the Xiangjiaba Reservoir (XJB), a river valley dammed reservoir in the upper Yangtze River, China. The model explained the relative contributions of the four aspects to reservoir CH4 production and accumulation. Approximately 78% of the CH4 concentration was contributed by the decomposition of flooded organic matter during the first 10 years after impoundment. However, the contribution of flooding faded away after 10 years of impoundment. With the increase in reservoir age, sedimentation of OC dominantly determined the reservoir CH4 production and accumulation. Scenario analysis of the XJB's life cycle demostrated that the CH4 concentration in the XJB would reach its peak approximately 70 - 80 years after impoundment. In the cascade system, the upstream reservoir will help to reduce sediment OC input, and to mitigate downstream reservoir CH4 production and accumulation. Our effort provided a new modeling approach for long-term management strategies to reduce reservoir CH4 emissions under global change.

Development of a multi-route physiologically based pharmacokinetic (PBPK) model for nanomaterials: a comparison between a traditional versus a new route-specific approach using gold nanoparticles in rats

BackgroundPhysiologically based pharmacokinetic (PBPK) modeling is an important tool in predicting target organ dosimetry and risk assessment of nanoparticles (NPs). The methodology of building a multi-route PBPK model for NPs has not been established, nor systematically evaluated. In this study, we hypothesized that the traditional route-to-route extrapolation approach of PBPK modeling that is typically used for small molecules may not be appropriate for NPs. To test this hypothesis, the objective of this study was to develop a multi-route PBPK model for different sizes (1.4–200 nm) of gold nanoparticles (AuNPs) in adult rats following different routes of administration (i.e., intravenous (IV), oral gavage, intratracheal instillation, and endotracheal inhalation) using two approaches: a traditional route-to-route extrapolation approach for small molecules and a new approach that is based on route-specific data that we propose to be applied generally to NPs.ResultsWe found that the PBPK model using this new approach had superior performance than the traditional approach. The final PBPK model was optimized rigorously using a Bayesian hierarchical approach with Markov chain Monte Carlo simulations, and then converted to a web-based interface using R Shiny. In addition, quantitative structure–activity relationships (QSAR) based multivariate linear regressions were established to predict the route-specific key biodistribution parameters (e.g., maximum uptake rate) based on the physicochemical properties of AuNPs (e.g., size, surface area, dose, Zeta potential, and NP numbers). These results showed the size and surface area of AuNPs were the main determinants for endocytic/phagocytic uptake rates regardless of the route of administration, while Zeta potential was an important parameter for the estimation of the exocytic release rates following IV administration.ConclusionsThis study suggests that traditional route-to-route extrapolation approaches for PBPK modeling of small molecules are not applicable to NPs. Therefore, multi-route PBPK models for NPs should be developed using route-specific data. This novel PBPK-based web interface serves as a foundation for extrapolating to other NPs and to humans to facilitate biodistribution estimation, safety, and risk assessment of NPs.

Same stimulus, same temporal context, different percept? Individual differences in hysteresis and adaptation when perceiving multistable dot lattices.

How we perceptually organize a visual stimulus depends not only on the stimulus itself, but also on the temporal and spatial context in which the stimulus is presented and on the individual processing the stimulus and context. Earlier research found both attractive and repulsive context effects in perception: tendencies to organize visual input similarly to preceding context stimuli (i.e., hysteresis, attraction) co-exist with tendencies that repel the current percept from the organization that is most dominant in these contextual stimuli (i.e., adaptation, repulsion). These processes have been studied mostly on a group level (e.g., Schwiedrzik et al., 2014). Using a Bayesian hierarchical model comparison approach, the present study (N = 75) investigated whether consistent individual differences exist in these attractive and repulsive temporal context effects, with multistable dot lattices as stimuli. In addition, the temporal stability of these individual differences in context effects was investigated, and it was studied how the strength of these effects related to the strength of individual biases for absolute orientations. The results demonstrate that large individual differences in the size of attractive and repulsive context effects exist. Furthermore, these individual differences are highly consistent across timepoints (one to two weeks apart). Although almost everyone showed both effects in the expected direction, not every single individual did. In sum, the study reveals differences in how individuals combine previous input and experience with current input in their perception, and more generally, this teaches us that different individuals can perceive identical stimuli differently, even within a similar context.

A hierarchical Bayesian approach to dynamic ordinary differential equations modeling for repeated measures data on wheat growth

Experimental data collected on growth and development of plants over a growing season are typically analyzed using a linear mixed model, analogous to a hierarchical linear model in a Bayesian setting. Alternative modeling approaches for repeated measures data involve non-linear models such as logistic regression and ecophysiological dynamic models based on a system of ordinary differential equations (ODE). Yet, current implementations of ODE models are mostly deterministic in nature, which negates recognition of uncertainty in the data generation process and thus impairs inference and prediction. The primary objective of this study was to demonstrate the use of a dynamic ODE model within a Bayesian framework to make stochastic inference on system-level parameters. A secondary objective was to compare the predictive performance of an ODE model relative to methodologies more commonly used for repeated measures data from designed experiments, namely hierarchical linear models and hierarchical non-linear models. Using a hierarchical Bayesian implementation, we fit all three types of models to data on leaf area index (LAI) and biomass from a winter wheat dataset. In the context of this application, none of the modeling approaches clearly outperformed any other in terms of goodness of fit or prediction accuracy as indicated by similar posterior median values for root mean squared error (RMSE), Willmott’s agreement index (d), and Nash-Sutcliffe efficiency (NSE). The prediction statistics for the ODE, linear, and non-linear models respectively, were: RMSEp of 1.38, 1.14, and 1.19; dp of 0.91, 0.93, and 0.93; and NSEp of 0.69, 0.78, and 0.76 for LAI and RMSEp of 274.08, 253.04, and 207.63; dp of 0.95, 0.95, and 0.97; and NSEp of 0.82, 0.84, and 0.89 for biomass. The dynamic ODE model enabled biologically meaningful system-level inferences relevant to the research questions that were not possible when using the hierarchical linear or non-linear modeling approaches.

On Hierarchical Bayesian Spatial Small Area Model for Binary Data under Spatial Misalignment

Small area models have become popular methods for producing reliable estimates for sub-populations (small geographic areas in this study). Small area modeling may be carried out via model-assisted approaches within the model-based approaches or design-based paradigm. When there are medium or large samples, a model-assisted approach may be reliable. However, when data are scarce, a model-based technique may be required. Model-based Bayesian analysis is popular for its ability to combine information from several sources as well as taking account uncertainties in the analysis and spatial prediction of spatial data. Nevertheless, things become more complex when the geographic boundaries of interest are misaligned. Some authors have addressed the problem of misalignment under hierarchical Bayesian approach. In this study, we developed non-trivial extension of existing hierarchical Bayesian model for a binary outcome variable under spatial misalignment with three contributions. First, the model uses unit-level survey data and area-level auxiliary data to predict the posterior mean proportion spatially at the second geographic area level. Second, the linking model is changed to logit-normal model in the proposed model. Lastly, the mean process was considered to overcome the multicollinearity between the true predictors and the spatial random effect. Sensitivity analysis was also done via simulation.

The effect of weather and climate on dengue outbreak risk in Peru, 2000-2018: A time-series analysis.

BackgroundDengue fever is the most common arboviral disease in humans, with an estimated 50-100 million annual infections worldwide. Dengue fever cases have increased substantially in the past four decades, driven largely by anthropogenic factors including climate change. More than half the population of Peru is at risk of dengue infection and due to its geography, Peru is also particularly sensitive to the effects of El Niño Southern Oscillation (ENSO). Determining the effect of ENSO on the risk for dengue outbreaks is of particular public health relevance and may also be applicable to other Aedes-vectored viruses.MethodsWe conducted a time-series analysis at the level of the district-month, using surveillance data collected from January 2000 to September 2018 from all districts with a mean elevation suitable to survival of the mosquito vector (<2,500m), and ENSO and weather data from publicly-available datasets maintained by national and international agencies. We took a Bayesian hierarchical modeling approach to address correlation in space, and B-splines with four knots per year to address correlation in time. We furthermore conducted subgroup analyses by season and natural region.ResultsWe detected a positive and significant effect of temperature (°C, RR 1.14, 95% CI 1.13, 1.15, adjusted for precipitation) and ENSO (ICEN index: RR 1.17, 95% CI 1.15, 1.20; ONI index: RR 1.04, 95% CI 1.02, 1.07) on outbreak risk, but no evidence of a strong effect for precipitation after adjustment for temperature. Both natural region and season were found to be significant effect modifiers of the ENSO-dengue effect, with the effect of ENSO being stronger in the summer and the Selva Alta and Costa regions, compared with winter and Selva Baja and Sierra regions.ConclusionsOur results provide strong evidence that temperature and ENSO have significant effects on dengue outbreaks in Peru, however these results interact with region and season, and are stronger for local ENSO impacts than remote ENSO impacts. These findings support optimization of a dengue early warning system based on local weather and climate monitoring, including where and when to deploy such a system and parameterization of ENSO events, and provide high-precision effect estimates for future climate and dengue modeling efforts.

CASE-FATALITY RATE BY COVID-19: A HIERARCHICAL BAYESIAN ANALYSIS OF COUNTRIES IN DIFFERENT REGIONS OF THE WORLD

The main goal of this study is the statistical analysis of deaths/cases epidemiologically defined as Case-Fatality Rate (CFR) due to novel coronavirus (SARSCoV-2) for 113 countries in different regions of the world in presence of some economic, health and social factors. The considered dataset refers to the accumulated daily counts of reported cases and deaths for a period ranging from the beginning of the COVID-19 pandemics in each country until July 25, 2020 the final follow-up day period. A binomial logistic regression model in presence of a random effect is assumed in the data analysis. The statistical analysis is considered under a hierarchical Bayesian approach using MCMC (Markov Chain Monte Carlo) methods do get the posterior summaries of interest.The results we found are interesting considering the epidemiological interpretation, which could be of great interest to epidemiologists, health authorities, and the general public in the face of a complex pandemic in all its aspects, like the one we are experiencing.