Optimal control of a delayed SIRC epidemic model with saturated incidence rate

In this paper, we present a susceptible‐infected‐recovered cross‐immune (SIRC) epidemic model, which describes Influenza A and analyzes the SIRC epidemic model through the optimal control theory and mathematical analysis. We show the existence of an optimal control pair for the optimal control problem by using Pontryagin's maximum principle with delay and derive the optimality condition. Finally, numerical simulation is carried out to verify our theoretical results.