Global Analysis of a Spatiotemporal Cellular Model for the Transmission of Hepatitis C Virus With Hattaf-Yousfi Functional Response

Abstract

This paper carries out a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both absorption phenomenon and diffusion of virions, infected and uninfected hepatocytes in the liver. Firstly, we prove the boundedness of the potential solutions, global existence, uniqueness, and positivity of the obtained initial value and boundary problem solution. Then, the dynamical behaviour of the model is entirely determined by a threshold parameter called the basic reproduction number denoted R₀. We show that the uninfected spatially homogeneous equilibrium of the model is globally asymptotically stable if R₀≤1 by using the direct Lyapunov method. The latter means that the HCV infection is cleared, and the disease dies out. Also, the global asymptotical properties stability of the infected spatially homogeneous equilibrium of the model are studied via a skilful construction of a suitable Lyapunov functional. It means that the HCV infection persists in the host, and the infection becomes chronic. Finally, numerical simulations are performed to support the obtained theoretical results.