Stability of a dengue epidemic model with independent stochastic perturbations

Abstract

Dengue is a vector-borne disease mainly affecting tropical and subtropical regions. The transmission of dengue virus is affected by many stochastic factors. Hence, we incorporated stochastic perturbations into the framework of a deterministic compartmental model. For this stochastic differential equation model, we introduced an approximate analogue of the basic reproduction number to explore the existence of the almost sure exponential stability of disease free equilibrium. We proved the existence and uniqueness of a positive solution for the stochastic differential equation model, and derived stability conditions by using suitable Lyapunov functions. Numerical simulations for the stochastic differential equation model of dengue virus transmission were presented to illustrate our mathematical findings. The analysis for determining whether the disease free equilibrium is almost surely exponentially stable in stochastic settings can be applied to the analysis of many other vector-borne transmissions.