Travel-blocking Optimal Control Policy on Borders of a Chain of Regions Subject to SIRS Discrete Epidemic Model
Sara Bidah
Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss EL HARTI B.P: 7955-Ben M’Sik 20800 Casablanca, Morocco.
Mostafa Rachik
Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss EL HARTI B.P: 7955-Ben M’Sik 20800 Casablanca, Morocco.
Omar Zakary *
Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss EL HARTI B.P: 7955-Ben M’Sik 20800 Casablanca, Morocco.
Hamza Boutayeb
Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss EL HARTI B.P: 7955-Ben M’Sik 20800 Casablanca, Morocco.
Ilias Elmouki
Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Avenue Commandant Driss EL HARTI B.P: 7955-Ben M’Sik 20800 Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
With thousands of people moving from one area to another day by day, in a chain of regions tightly more interconnected than other regions in a given large domain, an epidemic may spread rapidly around it from any point of borders. It might be sometimes urgent to impose travel restrictions to inhibit the spread of infection. As we aim to protect susceptible people of this chain to contact infected travelers coming from its neighbors, we follow the so-called travel-blocking vicinity optimal control approach with the introduction of the notion of patch for representing our targeted group of regions when the epidemic modeling framework is in the form of a Susceptible-Infected-Removed-Susceptible (SIRS) discrete-time system to study the case of the removed class return to susceptibility because of their short-lived immunity. A discrete version of the Pontryagin’s maximum principle is employed for the characterization of the travel-blocking optimal control. Finally, with the help of discrete progressive-regressive iterative schemes, we provide cellular simulations of an example of a domain composed with 100 regions and where the targeted chain includes 7 regions.
Keywords: Multi-regions model, epidemic model, optimal control, travel-blocking, patches, SIRS model, discrete-time model