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

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

MMC.
2023;
Volume 10, Number 4
: pp. 1071–1083
https://doi.org/10.23939/mmc2023.04.1071
Received: November 21, 2022
Revised: November 21, 2023
Accepted: November 23, 2023

Mathematical Modeling and Computing, Vol. 10, No. 4, pp. 1071–1083 (2023)

Authors:
  1. Y. Benfatah
  2. I. Khaloufi
  3. H. Boutayeb
  4. H. Laarabi
  5. M. Rachik
1
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco
2
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco
3
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco
4
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco
5
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco

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.

mathematical model
discrete-time systems
SIRS model
optimal control
contagious virus
Pontryagin maximum
zones evolution
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