Bayesian dynamic modeling of time series of dengue disease case counts

Abstract

The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

Markov Switching Integer-Valued Generalized Auto-Regressive Conditional Heteroscedastic Models for Dengue Counts

“…Martínez‐Bello et al . () modelled dengue time series data by using lag 1 meteorological variables. Alternatively, though, we can also choose weekly total precipitation (cumulative rainfall) and weekly average temperature as covariates.…”

“….5/ These conditions ensure the stationary and positivity of each intensity (2) when considering pure INGARCH models (Chen and Lee, 2017). Martínez-Bello et al (2017) modelled dengue time series data by using lag 1 meteorological variables. Alternatively, though, we can also choose weekly total precipitation (cumulative rainfall) and weekly average temperature as covariates.…”

“…We can handle the 'trend' effects, mentioned in Martínez-Bello et al (2017), by those coefficients via state 2. We assume the stability conditions of equation (6) as follows: Chen and Lee (2017)).…”

“…Although the rainy season varies slightly from region to region and is largely dominated by monsoons, it generally lasts from May or June to October. Studies also ascertain the important role that climatological factors such as temperature and precipitation have on weekly dengue counts (Chareonsook et al, 1999;Guha-Sapir and Schimmer, 2005;Hsieh and Chen, 2009;Hii et al, 2009;Limkittikul et al, 2014;Martínez-Bello et al, 2017).…”

Inferring the ecological drivers of arboviral outbreaks

“…However these deterministic frameworks fail to capture the inherent stochasticity and spatio-temporal heterogeneities of arboviral disease, and place strong implicit assumptions on vector ecology. Although discrete-time statistical transmission models (Li et al, 2018), such as Bayesian hierarchical dynamic Poisson models (Martínez-Bello et al, 2017), spatio-temporal risk models (Lowe et al, 2014;Martínez-Bello et al, 2018), and mixed models (Lowe et al, 2017), encapsulate the stochastic dynamics of arboviruses, they fail to capture the associations between epidemiological determinants and essential transmission drivers. Individual based models are arguably better suited to capture the spatio-temporal dynamics of arboviral disease whilst allowing for an unrestricted relationship between extrinsic and intrinsic factors.…”