New automated optimal vaccination control with a multi-region SIRS epidemic mode

Abstract

Many mathematical models describing the evolution of infectious diseases underestimate the effect of the Spatio-temporal spread of epidemics. Currently, the COVID-19 epidemic shows the importance of taking into account the spatial dynamic of epidemics and pandemics. In this paper, we consider a multi-region discrete-time SIRS epidemic model that describes the spatial spread of an epidemic within different geographical zones assumed to be connected with the movements of their populations (cities, towns, neighbors...).

Judging by the fact that there are several restrictions in medical resources and some delay in decision-making, the authorities and health decision-makers must define a threshold of infections in order to determine if a zone is epidemic or not yet. We propose a new approach of optimal control by defining new importance functions to identify affected zones and then the need for the control intervention. This optimal control strategy allows to reduce the infectious individuals and increase the number of recovered ones in the targeted domain and this with an optimal cost. Numerical results are provided to illustrate our findings by applying this new approach in the Casablanca-Settat region of Morocco. We investigate different scenarios to show the most effective scenario, based on thresholds’ values.