Analysis and Optimal Control of a Two-Strain SEIR Epidemic Model with Saturated Treatment Rate

In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strains with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as R1 and R2. The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when R1 and R2 are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin’s maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control.