Analysis of stochastic vector-host epidemic model with direct transmission

In this paper, we consider the stochastic vector-host epidemic model with direct transmission. First, we study the existence of a positive global solution and stochastic boundedness of the system of stochastic differential equations which describes the model. Then we introduce the basic reproductive number $\mathcal{R}^s_0$ in the stochastic model, which reflects the deterministic counterpart, and investigate the dynamics of the stochastic epidemic model when $\mathcal{R}^s_0 1$. In particular, we show that random effects may lead to extinction in the stochastic case while the deterministic model predicts persistence. Additionally, we provide conditions for the extinction of the infection and stochastic stability of the solution. Finally, numerical simulations are presented to illustrate some of the theoretical results.