Global dynamics for discrete-time analog of viral infection model with nonlinear incidence and CTL immune response

摘要

In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers R 0 $R_{0}$ and R 1 $R_{1}$ are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. By using the Lyapunov functions and linearization methods, the global stability of the equilibria for the model is established. That is, when R 0 ≤ 1 $R_{0}leq1$ then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption ( A 4 ) $(A_{4})$ when R 0 1 $R_{0}1$ and R 1 ≤ 1 $R_{1}leq1$ then the no-immune equilibrium is globally asymptotically stable and when R 0 1 $R_{0}1$ and R 1 1 $R_{1}1$ then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption ( A 4 ) $(A_{4})$ does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.