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In this paper, the aim is to analyze the global dynamics of Hepatitis C Virus (HCV) cellular mathematical model under therapy with uninfected hepatocytes proliferation. We prove that the solution of the model with positive initial values are global, positive and bounded. In addition, firstly we show that the model is locally asymptotically stable at free virus equilibrium and also at infected equilibrium. Secondly we show that the model is globally asymptotically stable at the free virus equilibrium by using an appropriate lyapunov function.

Global Dynamics of an Hepatitis C Virus Mathematical Cellular Model with a Logistic Term