A discrete mathematical model SIRS with the evolution of regions to attack infectious diseases

Abstract

This paper presents a new SIRS mathematical model describing the evolution of an infectious disease, assuming that the spatial supports of this infection are also evolutionary and obey a compartmental model. We propose four control strategies to manage the spread of the disease among individuals and regions. The Pontryagin maximum principle is employed to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are conducted to validate the theoretical analysis using MATLAB.