A mathematical SIR model on the spread of infectious diseases considering human immunity

Marouane Lafif, Issam Khaloufi, Youssef Benfatah, Jamal Bouyaghroumni, Hassan Laarabi, Mostafa Rachik

Abstract


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.


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Published: 2022-07-25

How to Cite this Article:

Marouane Lafif, Issam Khaloufi, Youssef Benfatah, Jamal Bouyaghroumni, Hassan Laarabi, Mostafa Rachik, A mathematical SIR model on the spread of infectious diseases considering human immunity, Commun. Math. Biol. Neurosci., 2022 (2022), Article ID 69

Copyright © 2022 Marouane Lafif, Issam Khaloufi, Youssef Benfatah, Jamal Bouyaghroumni, Hassan Laarabi, Mostafa Rachik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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