Dynamic analysis and optimal control for a model of hepatitis C with treatment

A model for hepatitis C is formulated to study the effects of treatment and public concern on HCV transmission dynamics. The stability of equilibria and persistence of the model are analyzed, and an optimal control measure is performed to prevent the spread of HCV with minimal infected individuals and cost. The dynamical analysis reveals that the disease-free equilibrium of the model is asymptotically stable if the basic reproductive number R0 is less than unity. On the other hand, if R0>1, the disease is uniformly persistent. Numerical simulations are conducted to investigate the influence of different vital parameters on R0. For the corresponding optimality system, the optimal solution is discussed by Pontryagin Maximum Principle, and the comparisons of model-predicted consequences with control or not are presented.