Global properties of a virus dynamics model with self-proliferation of CTLs

Cuicui Jiang,Guohong Zhang,Kaifa Wang,Huan Kong

doi:10.5206/mase/13822

Abstract

A viral infection model with self-proliferation of cytotoxic T lymphocytes (CTLs) is proposed and its global dynamics is obtained. When the per capita self-proliferation rate of CTLs is sufficient large, an infection-free but immunity-activated equilibrium always exists and is globally asymptotically stable if the basic reproduction number of virus is less than a threshold value, which means that the immune effect still exists though virus be eliminated. Qualitative numerical simulations further indicate that the increase of per capita self-proliferation rate may lead to more severe infection outcome, which may provide insight into the failure of immune therapy.

Highlights

Outbreaks of viral infection have become a major global health concern
Since we are interested in the dynamics of viral infection, and not the initial processes of infection, we assume that the initial condition of (1.2) has the form x(0) > 0, y(0) > 0, v(0) > 0 and z(0) > 0
The complete global properties of system (1.2) have been obtained in Figure 1, it is noted that the immunity-activated infection equilibrium E3 or E4 is related to the parameters of selfproliferation of cytotoxic T lymphocytes (CTLs) (r and m) from Proposition 2.1

Summary

Introduction

Outbreaks of viral infection have become a major global health concern. Different kinds of virus, such as hepatitis B virus (HBV), hepatitis C virus (HCV), human immunodeficiency virus (HIV), Ebola Virus and Zika Virus, have been associated with severe outcomes. On HBV infection, Nowak et al [13] first proposed a basic three-dimensional viral infection model within-host. Nowak et al [14] further proposed the following four-dimensional system with the cytotoxic T lymphocytes (CTLs) population based on the basic model:. Free virus are produced from infected cells at rate ky and die at rate uv. CTLs are produced at rate cyz due to the stimulation of infected cells, and die at rate d3z. When r = 0, i.e., without self-proliferation of CTLs, (1.2) has been completely analyzed in [10] if there is not explicit dynamics of free virus under a plausible quasi steady-state assumption. To explore the effects of the recruitment of immune responses on virus infection, the main contribution of the present paper is to obtain the complete global properties of (1.2) when r > 0

Global dynamics analysis

Numerical simulations

Discussion