Stationary Distribution of a Stochastic HIV Model with Nonlinear Immune Response Function
In this paper,a sufficient condition for the existence of unique ergodic stationary distribution in a stochastic HIV model with target cell growth and nonlinear immune response is given.Stochastic Lyapunov analysis method and Ito formula are used to prove the stochastic HIV model.By constructing a novel combination of Lyapunov functions,it is proved that the stochastic HIV model has a unique ergodic stationary distribution when the critical thresholds basic reproduction number RS0＞1 and virus reproduction number RS1＞1 are established.The existence of an ergodic stationary distribution implies that all individuals can coexist in the long run.
Stochastic HIV modelUncertaintyNonlinear immune responseLyapunov functionStationary distribution
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