Global analysis for a delayed HCV model with saturation incidence and two target cells

Abstract

In this paper, a mathematical model describing the dynamics of hepatitis C virus infection is proposed. Distributed delay, saturation incidence and CTL immune response in the liver and extrahepatic tissue are taken into account in the model. The model is rigorously analyzed, and a detailed global stability analysis is performed. A novel method is used to analyze the existence of the equilibria. By constructing suitable Lyapunov functionals and using LaSalle-type theorem for delay differential equations, sufficient condition for the global asymptotic stability of the equilibrium point is obtained. The results show that when R0<1, there is no virus and immune responses existed in the end; when R1<1<R0, the virus survives, but immune response gradually disappears; when R0>1 and R1>1, the system will be globally stable with both virus and immune responses. Numerical analysis confirms the theorems and suggests that time delay play a positive role in virus infection and virus production process in order to eliminate infected liver and blood cells and virus. Furthermore, the simulation also explains the personalized difference in clinical test value.