Stochastic Bayesian Runge-Kutta method for dengue dynamic mapping

Dengue Hemorrhagic Fever (DHF) is still a threat to humanity that cause death and disability due to changes in environmental and socioeconomic conditions, especially in tropical areas. A critical assessment of the models and methods is necessary. The vital role of stochastic processes of infectious disease research in Bayesian statistical models helps provide an explicit framework for understanding disease transmission dynamics between hosts (humans) and vectors (mosquitoes). This research presents a Bayesian stochastic process for the cross-infection SIR-SI model as a differential equation (susceptibility–infection–recovery for the human population; susceptible–infectious for the vector population) for the dynamic transmission of DHF. Given the difficulties of solving the differential equations precisely, we propose a computational model to approach the solution based on the Runge-Kutta family approach, namely the Euler and the four-order Runge-Kutta methods. The methods used for the discretization process of the SIR-SI model for computational process needs. For comparison purposes, we use a monthly DHF dataset of 10 Kendari, Indonesia, districts from 2019 to 2021. Parameter estimation of the Bayesian SIR-SI model based on the Euler and four-order Runge-Kutta method was updated using Markov Chain Monte Carlo (MCMC) Bayesian. The Euler and four-order Runge-Kutta methods have converged at 10,000 iterations with burn-in 80,000. The numerical simulation results show that the four-order Runge-Kutta approach has the slightest deviance, 106.5. Therefore, this approach is the best one. The relative risk analysis shows that the dynamics of DHF cases fluctuate from January to July every year. However, from January to May, there was a high consistency of DHF cases. Two districts with high case consistency were found, namely Kadia and Wua-Wua. Furthermore, because the spread of DHF cases has a spatial effect, the Kadia and Wua-Wua districts need serious attention to suppress the rate of reach of DHF in Kendari City. Intensive observation and intervention in the Kadia and Wua-Wua districts should be carried out in early January to stop the breeding of mosquito larvae. In other neighbourhoods such as Puwatu, Kambu and Kendari Barat, the DHF cases occur temporally as the impacts of DHF cases in the Kadia and Wua-Wua districts. It may facilitate the statisticians to develop further models to adopt a better understanding to control the DHF dynamically. In brief,