The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment

Abstract

Abstract A stochastic viral infection model with two modes of transmission and immune impairment is proposed in this paper, which contains four variables; uninfected cells, infected cells, virus particles and cytotoxic T lymphocytes. We first investigate the exponential stability of the model, and further give sufficient conditions for the extinction and persistence of the disease. By constructing a suitable stochastic Lyapunov function, we then prove the existence of a unique ergodic stationary distribution of the model. More importantly, a stochastic threshold R 0 W is presented, which plays the similar role as R 0 in determining the persistence and extinction of the infected cells. As an application of the method proposed in this paper, the existence of an ergodic stationary distribution and a stochastic positive periodic solution of the model under the influence of colored noise and seasonal fluctuations are studied respectively. Finally, we carry out some numerical simulations, showing that environmental noise may suppress the spread of disease.