SIS multi-regions discrete Influenza pandemic model and travel-blocking vicinity optimal control strategy on two forms of patch

Abstract

In this paper, we study the multi-region sis discrete-time model which describesthe spread of an influenza pandemic in interconnected regions via infection mobility.Our objective from this model, is to suggest in a first case of simulations,the so-called travel-blocking vicinity optimal control strategy aiming to protectsusceptible people of a complex of regions tightly close one to each other,while in a second case, we discuss the importance of such strategies when theregions aiming to control are very dispersed. In the theoretical part of the paper,we utilize a discrete version of the pontryagin’s maximum principle for thecharacterization of the travel-blocking optimal control. As for the numericalpart, we program the resolution of our multi-points boundary value problem usingdiscrete progressive-regressive iterative schemes, in an example of a domaincomposed with 100 regions and where the targeted patch includes 4 regions, inthe first time grouped and in a second time, dispersed.