About: 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.   Goto Sponge  NotDistinct  Permalink

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  • 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.
subject
  • Virology
  • Viruses
  • Differential calculus
  • Stability theory
  • Dynamical systems
  • Statics
  • Elementary shapes
  • 1898 in biology
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