Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity

In this paper, we will study mathematically and numerically the dynamics of the hepatitis C virus disease with the consideration of two fundamental modes of transmission of the infection, namely virus-to-cell and cell-to-cell. In our model, we will take into account the role of cure rate of the infected cells and the effect of the adaptive immunity. The model consists of five nonlinear differential equations, describing the interaction between the uninfected cells, the infected cells, the hepatitis C virions and the adaptive immunity. This immunity will be represented by the humoral and cellular immune responses. This work begins with proving the non-negativity and the boundedness of solutions and determining the basic reproduction number. Secondly, five equilibria are established, the local stability analysis for all the equilibria is demonstrated theoretically and numerically. Finally, we have concluded that the numerical results are coherent with our theoretical postulations.