<p>In this paper, a fractional-order HCV model with saturation incidence rate and antibody immune response is constructed and analyzed. Two cases are considered: without control and with optimal control. For the first case, the existence and uniqueness of the positive solution are proved firstly, and then, the sufficient conditions for the local stability of two equilibriums of the system are obtained; further, the disease-free equilibrium is shown to be globally asymptotically stable by constructing an appropriate Lyapunov function. For the second case, dual control measures are included in the model, which represent the therapeutic hepatitis C inhibitor ITX5061 and DAAs. By using Pontryagin’s Maximum Principle, the optimal solution is obtained. For both cases, some numerical simulations are performed to validate the theoretical results. Finally, some discussions and conclusions are listed at the end.</p>