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

Wang, Jianpeng; Teng, Zhidong; Miao, Hui

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 [Formula: see text] and [Formula: see text] 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 [Formula: see text] then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption [Formula: see text] when [Formula: see text] and [Formula: see text] then the no-immune equilibrium is globally asymptotically stable and when [Formula: see text] and [Formula: see text] then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption [Formula: see text] does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.