Pandemics have shaped human history and they remain with us today. Recognizing how these diseases spread can therefore help identify specific disease control strategies. Classical mathematical models describing the evolution of infectious diseases underestimate the effect of the spatio-temporal spread of epidemics. Currently, the COVID-19 pandemic shows the importance of taking into account the spatial dynamics of epidemics and pandemics and the need for new control strategies including vaccinations, awareness and travel restrictions. Here, we consider a SIRS discrete-time multi-regional epidemic model that describes the spatial spread of an epidemic in different geographic areas believed to be related to movements of their populations. We propose a novel approach of optimal control by defining new functions of importance to identify affected areas based on infection thresholds that determine whether the need for a control intervention or not. Numerical results are provided to illustrate our results by applying this new approach in adjacent areas of Morocco, that is, the Casablanca-Settat regions. We study different scenarios to show the most efficient scenario, based on the threshold values.
On the Optimal Vaccination and Travel-restriction Controls with a Discrete Multi-region Sirs Epidemic Model