Environmental variability in a stochastic HIV infection model

Abstract

In this paper, a stochastic HIV infection model with the Ornstein–Uhlenbeck process is established and studied. It is assumed that the death rate of healthy CD4+ T cells satisfies the Ornstein–Uhlenbeck process. First, we verify that the stochastic model has an unique global solution for any initial value. Then, using Markov semigroup technique, we obtain the sufficient criteria for the existence of a stable stationary distribution to the stochastic system, which reflects the strong persistence of all CD4+ T cells and HIV virus particles. Furthermore, it is deduced that the above global solution around the endemic equilibrium follows an unique probability density function by solving the corresponding Fokker–Planck equation and having to apply our developed algebraic equation theory. The necessary conditions for the exponential extinction of HIV infection are established for completeness. Finally, several numerical simulations are provided to validate our theories.