Dynamic analysis and optimal control of a fractional order HCV model with immune response

In this paper, a class of Captuo fractional order derivative HCV model with immune response is established and analyzed.Two cases are considered: in the first case, the control function is a constant, and in the second case, the control function is a variable.For the constant control system, the existence and uniqueness of the system solution are proved, the sufficient conditions for the existence of three equilibrium points are obtained, and the local stability of the system at these equilibrium points is proved, among which the bistable phenomenon occurs at the positive equilibrium.For the optimal control system, Pontryagin's maximum principle is employed to analyze the optimal control and derive the optimal solution.In order to validate the theoretical results, numerical simulations are performed for both cases.The results of these simulations are discussed and concluded in the final section of the paper.