Mathematical analysis of dengue stochastic epidemic model

Dengue is a vector-borne disease mainly affecting the tropical and subtropical regions. The transmission as well as the control of dengue virus is not deterministic while stochastic due to various factors. We use a stochastic Markovian dynamics approach to describe the spreading of dengue and the threshold of the disease. The coexistence space is composed by human and mosquito populations. First, we show that there is a global existence and positivity of the solution. Then, we calculate the basic stochastic reproduction number R0s as a threshold that will determine the extinction or persistence of the disease. If R0s 1, some sufficient condition for the existence of stationary distribution is obtained. Finally, numerical simulations for the stochastic differential equations model describing the dynamics of dengue virus were presented to illustrate our mathematical findings.