Résumé
In this paper, we propose a mathematical model of infection by infectious diseases, taking into account the division of the population according to the criteria of immunity. Our objective is to demonstrate the positive effect of this idea against the different epidemics. We have proposed two strategies to reduce the great human and material losses caused by these diseases, respectively awareness programs on the importance of the exercise of sport and a healthy food to increase human immunity, treatment and health care for people with low immunity. The Pontryagin maximum principle is applied to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB. © 2022 the author(s).
Résumé
In this paper, we present a new mathematical model to describe the evolution of an infectious disease in regions and between individuals. For this purpose we considered two systems, the first one for humans Si Ii Ri, where Si represents the number of susceptible, Ii of infected and Ri of cured. The second system ZiSZIiZRi represents the different types of regions, where Zis is the number of susceptible regions, where there are only susceptible people, after visiting an infected person, a susceptible region is likely to be infected, which we will note ZiI, the last compartment ZiR denotes the infected regions, which are restored after the recovery of all infected people. In addition, we considered three control strategies u, v and w to control the spread of the virus within regions and between individuals. Numerical examples are provided to illustrate the effectiveness of our proposed control strategy. © 2022 the author(s).