COVID-19 SPATIOTEMPORAL SIR MODEL: REGIONAL OPTIMAL CONTROL APPROACH

In the present work, we consider a spatio-temporal model to describe the evolution of covid19 in an area Ω (Ω can be a city, a country,..). Taking into account the financial means of the considered country, we suppose that the number of available vaccines is destined to a region ω1 ⊆Ω (ω1 can be an industrial city, a university city. ..) and we suppose that the available treatments are dedicated to a region ω2 ⊆ Ω (ω2 can be a military city,..), it is not excluded that ω1 = ω2 . To minimize the number of infection with minimal cost, we apply an optimal regional control strategy to stop the death of infected individuals in the considered area. Much of this work has been devoted to mathematical study, where the existence of the optimal controls and the solutions of the state system are proven, an optimal control characterization in terms of state and adjoint functions are provided, and the optimality system is solved numerically using a forward-backward sweep method. Our numerical results suggest that when vaccination and treatment procedures are used together, the control approach becomes more effective in protecting a specific region from epidemic transmission from neighboring regions. © 2022 the author(s).

OPTIMAL CONTROL FOR A DISCRETE TIME EPIDEMIC MODEL WITH ZONES EVOLUTION

In this paper, we present a new mathematical model to describe the evolution of an infectious disease in regions and between individuals. For this purpose we considered two systems, the first one for humans Si Ii Ri, where Si represents the number of susceptible, Ii of infected and Ri of cured. The second system ZiSZIiZRi represents the different types of regions, where Zis is the number of susceptible regions, where there are only susceptible people, after visiting an infected person, a susceptible region is likely to be infected, which we will note ZiI, the last compartment ZiR denotes the infected regions, which are restored after the recovery of all infected people. In addition, we considered three control strategies u, v and w to control the spread of the virus within regions and between individuals. Numerical examples are provided to illustrate the effectiveness of our proposed control strategy. © 2022 the author(s).

AUTOMATED OPTIMAL VACCINATION AND TRAVEL-RESTRICTION CONTROLS WITH A DISCRETE MULTI-REGION SIR EPIDEMIC MODEL

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.

ON THE OPTIMAL VACCINATION AND TRAVEL-RESTRICTION CONTROLS WITH A DISCRETE MULTI-REGION SIRS EPIDEMIC MODEL

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.

An automated optimal vaccination control with a multi-region sir epidemic model

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 there. Numerical results are provided to illustrate our findings by applying this new approach in two adjacent regions of Morocco, the Casablanca-Settat and Rabat-Salé-Kénitra regions. We investigate different scenarios to show the most effective scenario, based on thresholds’ values. © 2021 the author(s).