Automated optimal vaccination and travel-restriction controls with a discrete multi-region SIR epidemic model

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 contribution, we consider a multi-region discrete-time epidemic model that describes the spatial spread of an epidemic within different geographical zones assumed to be connected with the movements of their populations. Based on the fact that there are several limitations in medical resources, 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. Numerical results are provided to illustrate our findings by applying this new approach in two adjacent regions of Morocco, the Casablanca-Settat and Rabat-Sale-Kenitra regions. We investigate different scenarios to show the most effective scenario, based on thresholds’ values.