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

Zhidong Teng,Hui Miao,Jianpeng Wang

doi:10.1186/s13662-016-0862-y

Abstract

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} and 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}leq1 then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption (A_{4}) when R_{0}>1 and R_{1}leq1 then the no-immune equilibrium is globally asymptotically stable and when R_{0}>1 and R_{1}>1 then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption (A_{4}) does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.

Highlights

As is well known, viruses have caused the abundant types of epidemics and are alive almost everywhere on Earth, infecting people, animals, plants, and so on
There are a large number of diseases, which are caused by viruses for example: influenza, hepatitis, HIV, AIDS, SARS, Ebola, MERS
Many authors have studied continuous time viral infection models which are described by the differential equations

Summary

Introduction

Viruses have caused the abundant types of epidemics and are alive almost everywhere on Earth, infecting people, animals, plants, and so on. Proof It is clear that the equilibrium of model ( ) satisfies the following equation:

Results

Conclusion