A discrete mathematical modeling of transmission of COVID-19 pandemic using optimal control

Abstract

In this work, we present a study of optimal control strategies of a Novel Corona Virus Disease 2019 (COVID-19) spreading model in the discrete case. The targeted population is divided into six compartments SEICWCR namely (S) susceptible, (E) exposed, (I) infected, (C^W) infected with complication, (C) infected multimorbidity with complication and (R) recovered. We also proposed an optimal strategy to fight against the spread of COVID-19. We use four controls which represent the sensitization and prevention through the media and education for the susceptible individuals, quarantined the infected at home, quarantined the infected with complication at the hospital, quarantined the infected multimorbidity with complication at the hospital with requirement breathing assistance. Theoretically, we have proved the existence of optimal controls, and a characterization of the controls in terms of states and adjoint functions principally based on Pontryagin’s maximum principle. To clarify the efficiency of our theoretical results, we provide numerical simulations for numerous scenarios. Therefore, the obtained results affirm the performance of the optimization approach.