A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account

A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin's maximum principle is used to describe the optimal controls, and an iterative approach is used to solve the optimality system. Finally, numerical simulations are carried out in MATLAB to verify the theoretical analysis.