Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

摘要

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R-0 <= 1, then the solution of the stochastic system oscillates around the infection-free equilibrium E-0, while if R-0 > 1, then the solution of the stochastic system fluctuates around the infective equilibrium E*. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results. (C) 2017 Elsevier B.V. All rights reserved.