In this work, we propose and analyze a class of two temporal basic models describing Hepatitis C infection caused by Hepatitis C Virus (HCV) including two biological important aspects. The first model with only absorption and the second with absorption and intracellular delay. In the two proposed models, the disease transmission process is submitted in mass action principle. First of all, we investigate the model without a delay where we carry up the global analysis of the model. Secondly, we investigate the model with an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles. We established the local stability of the equilibria of the proposed models. By using suitable Lyapunov functionals and LaSalle’s invariance principle, we prove rigorously that if the basic reproduction ratio is less than unity, then the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, then the sufficient condition is derived for the global stability of the chronic-infection equilibrium. Finally, a numerical simulation is carried out to confirm theoretical results. Moreover, the model and main results presented in [11] are extended and generalized.

HCV infection, mass action principle, intracellular delay, absorption, Lyapunov methods, stability, numerical simulation.