Stochastic Runge-Kutta for numerical treatment of dengue epidemic model with Brownian uncertainty

The current challenge faced by the global research community is how to effectively address, manage, and control the spread of infectious diseases. This research focuses on conducting a dynamic system analysis of a stochastic epidemic model capable of predicting the persistence or extinction of the dengue disease. Numerical methodology on deterministic procedures, i.e. Adams method and stochastic/probabilistic schemes, i.e. stochastic Runge-Kutta method, is employed to simulate and forecast the spread of disease. This study specifically employs two nonlinear mathematical systems, namely the deterministic vector-borne dengue epidemic (DVBDE) and the stochastic vector-borne dengue epidemic (SVBDE) models, for numerical treatment. The objective is to simulate the dynamics of these models and ascertain their dynamic behavior. The VBDE model segmented the population into the following five classes: susceptible population, infected population, recovered population, susceptible mosquitoes, and the infected mosquitoes. The approximate solution for the dynamic evolution for each population is calculated by generating a significant number of scenarios varying the infected population's recovery rate, human population birth rate, mosquitoes birth rate, contaminated people coming into contact with healthy people, the mortality rate of people, mosquitos population death rate and infected mosquito contact rate with population that is not infected. Comparative evaluations of the deterministic and stochastic models are presented, highlighting their unique characteristics and performance, through the execution of numerical simulations and analysis of the results.