Stability Analysis of an Improved HBV Model with CTL Immune Response.

Mostafa Khabouze,Noura Yousfi,Khalid Hattaf

doi:10.1155/2014/407272

Mostafa Khabouze, Noura Yousfi + Show 1 more

Open Access

https://doi.org/10.1155/2014/407272

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Abstract

To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms. The local stability of the disease-free equilibrium and the chronic infection equilibrium is obtained via characteristic equations. Furthermore, the global stability of both equilibria is established by using two techniques, the direct Lyapunov method for the disease-free equilibrium and the geometrical approach for the chronic infection equilibrium.

Highlights

hepatitis B virus (HBV) infection is a major global health problem, which can lead to cirrhosis and liver cancer
To better understand the dynamics of the hepatitis B virus (HBV) infection, we introduce an improved HBV model with standard incidence function, cytotoxic T lymphocytes (CTL) immune response, and take into account the effect of the export of precursor CTL cells from the thymus and the role of cytolytic and noncytolytic mechanisms
Many mathematical models have been developed in order to understand the dynamics of HBV infection

Summary

Introduction

HBV infection is a major global health problem, which can lead to cirrhosis and liver cancer. We consider the model presented by Pang et al in [2] that is given by the following nonlinear system of differential equations:. Μz, where x(t), y(t), V(t), and z(t) are the numbers of uninfected target cells, infected cells, free virus, and CTL cells at time t, respectively. Infected cells die at a rate ay, return to the uninfected state by a nonlytic effector mechanism [3] at a rate qyz, and are killed by the CTL immune response at a rate pyz. CTL cells expand in response to viral antigen derived from infected cells at a rate cyz/(ω+y), where c is HBV-specific CTL stimulation rate and ω represents virus load for half-maximal CTL cells stimulation [4] and decay in the absence of antigenic stimulation at a rate μz.

Well Posedness and Steady States

Local Stability of Equilibria

Global Stability of Equilibria

Findings

Conclusion and Discussion