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Volume 20,     Number 4,     Winter 2012

 

GLOBAL STABILITY ANALYSIS OF A
GENERALIZED VIRUS DYNAMICS MODEL
WITH THE IMMUNE RESPONSE
K. HATTAF, N. YOUSFI AND A. TRIDANE

Abstract. The aim of this work is to study the global stability of a generalized model of a viral dynamic that includes the adaptive immune response, represented by Cytotoxic Lymphocyte T-cell (CTL-cell ). The incidence function introduced in this model is the generalization of a variety of viral models including HIV, influenza, HBV, and HCV. We show that the global stability of this model, using the Lyapunov function, is not only characterized by the basic reproduction number but also by what is called the basic defense number, which represents the level of the infection required to trigger the CTL response. In fact, if the basic defense number is bigger than one, we prove the global stability of the CTL-active equilibrium, which represents a chronic stage of the infection, where the CTL cells could also damage the healthy cells. Otherwise, we have another equilibria that represents the early state of the infection, where the adaptive immune response is not involved yet in the clearance of the infection and only the innate immune response is active.

 

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