Dynamical behaviors of the fractional order HCV model

In this paper, a fractional-order model of hepatitis C virus (HCV) with inhibition due to infection is studied. Based on the basic reproduction number, backward bifurcation of such model is investigated under some conditions. When the efficacy of interferon-alpha therapy is low, it is shown that the phenomenon of backward bifurcation will appear in the model. It means that there coexist disease-free and endemic equilibrium points. Then a critical basic reproduction number is given, which could be used as a threshold to control the virus. Using the generalized Lasalle invariant set principle, it is found that the disease-free equilibrium point of the model is globally asymptotically stable. The optimal efficacy of interferon-alpha therapy is also studied. Numerical simulations have been used to verify the theoretical analysis.