Modeling the Dynamics of Hepatitis C Virus and Immune System during Acute Infection

Abstract

In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune system has been studied. The paper intends to upgrade the model developed by Avendano et al.(2002) by including death of hepatocytes due to infection and spontaneous clearance of viruses by a noncytolytic process during acute stage of the HCV infection. The next generation matrix method has been applied to compute the basic reproductive number. Also, the stability analysis of the system has been performed for the existence of the disease free and endemic equilibrium states using Meltzer matrix, Routh-Hurwitz and Lyapunov methods. The results indicate that the disease free equilibrium state is locally asymptotically stable if, and unstable if.The endemic equilibrium state is both locally and globally asymptotically stable. We calculated the sensitivity indices of the dynamic threshold relating to each parameter in the model, where we found that the decrease of the rate of infection and the rate of generation of virions have the effect of lessening the infection, which suggests that the disease can be controlled when therapeutic intervention is done on these parameters.

Keywords: Hepatitis C virus, Immune system, Basic reproductive number, Disease-free equilibrium state, Endemic equilibrium state.