Dynamic analysis of stochastic virus infection model with delay effect

Abstract

This paper mainly investigates the dynamic behavior of virus infection model with delay effect influenced by external noise. First, a mathematical model describing the evolution of virus under the influences of stochastic noise and delay effect is developed. And necessary conditions for extinction and weak persistence are derived by Ito’s formula. A new basic reproduction number R˜0 for virus infection model with delay effect to determine whether extinction or persistence is given. It is found that the delay parameter τ affects the new basic reproduction number R˜0, and the behavior of extinction and survival of virus. Besides, the threshold for extinction of stochastic model is smaller than the one of deterministic model. In the end, stochastic simulations are applied to illustrate and test the theoretical conclusions.