Global Stability of Delayed Viral Infection Models with Nonlinear Antibody and CTL Immune Responses and General Incidence Rate.

Hui Miao,Zhidong Teng,Zhiming Li

doi:10.1155/2016/3903726

Hui Miao, Zhidong Teng + Show 1 more

Open Access

https://doi.org/10.1155/2016/3903726

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Abstract

The dynamical behaviors for a five-dimensional viral infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses, and nonlinear incidence rate are investigated. The threshold values for viral infection, antibody response, CTL immune response, CTL immune competition, and antibody competition, respectively, are established. Under certain assumptions, the threshold value conditions on the global stability of the infection-free, immune-free, antibody response, CTL immune response, and interior equilibria are proved by using the Lyapunov functionals method, respectively. Immune delay as a bifurcation parameter is further investigated. The numerical simulations are performed in order to illustrate the dynamical behavior of the model.

Highlights

In recent years, many authors have formulated and studied mathematical models which describe the dynamics of virus population in vivo
Motivated by the work in [1, 2, 20, 21], in the present paper we propose a general viral infection model with three time delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses, and nonlinear incidence rate dx (t) dt
In this paper we have considered an in-host model with intracellular delay τ1, virus replication delay τ2, and immune response delay τ3, given by (2) together with assumptions (H1)–(H4), which describes the dynamics among uninfected cells, infected cells, virus, CTL responses, and antibody responses

Summary

Introduction

Many authors have formulated and studied mathematical models which describe the dynamics of virus population in vivo. Where x, y, V, w, and z denote the concentrations of susceptible host cells, infected cells, free virus, antibody responses, and CTL immune responses, respectively. Motivated by the work in [1, 2, 20, 21], in the present paper we propose a general viral infection model with three time delays which describes the interactions of antibody, CTL immune responses, and nonlinear incidence rate dx (t) dt s. It is assumed that the death rates of the infected target cells, viruses, antibody, and CTLs depend on their concentrations. These rates are given by ag1(y), ug2(V), hg3(w), and bg4(z), respectively.

Preliminaries

Stability of Equilibrium E0

Numerical Simulations

Discussion