Study on the global stability and optimal control strategy of an epidemic model with consideration of the fear factor

In this paper, we investigate the impact of fear on the transmission and control of infectious diseases by formulating a three-dimensional compartmental model. Susceptible individuals are divided into two subclasses according to their fear susceptibility toward the disease. The analysis includes an examination of the basic reproduction number, discussion on the existence and global stability of disease-free and endemic equilibria, and the derivation of an optimal control strategy using Pontryagin’s Minimum Principle. Theoretical analysis and numerical simulations indicate that the presence of fear factor can effectively reduce the number of infections, but its impact on the optimal control strategy is weak.