3 - Global dynamics of an HCV model with full logistic terms and the host immune system

Abstract

In this chapter, we present a mathematical model that describes the dynamics of the hepatitis C virus (HCV) considering four populations: uninfected liver cells, infected liver cells, HCV, and T cells (cytotoxic T lymphocytes). The model incorporates logistic growth terms with distinct cell proliferation rates for both uninfected hepatocytes and infected hepatocytes. We show positivity and boundedness of the system solutions, and we calculate the basic reproduction number R0, which is a sharp threshold parameter for the outcomes of viral infections. Analysis of the model elucidates the existence of two equilibrium states: the uninfected state and the endemically infected state. Moreover, the uninfected state (called the disease-free equilibrium) is globally asymptotically stable whenever the basic reproduction number is less than unity. If R0>1, the system is uniformly persistent, the unique endemic equilibrium appears and is locally asymptotically stable. We analyze global stability of the positive equilibrium via Li-Muldowney's geometrical approach. Finally, we give some numerical simulations to justify our analytical results.