Mathematical modeling and optimal control strategy for a discrete time model of COVID-19 variants

Abstract

In this study, we analyze the transmission dynamics of several variants of Covid-19 that have appeared around the world. Our aim is to propose a discrete mathematical model that describes the dynamics of different infectious compartments, namely, Susceptible (S), Exposed (E), Individuals infected with the Alpha variant (I1), Individuals infected with the Beta variant (I2), Individuals infected with the Gamma variant (I3), Individuals infected with the Delta variant (I4), Hospitalized (H), Quarantined (Q) and Recovered (R). We also focus on the importance of people infected with the Alpha, Beta, Gamma and Delta variants, with the aim of finding optimal strategies to minimize the number of people infected with the different variants of Covid-19. We used three controls which represent: 1) awareness programs through media and civil society to urge uninfected people to stay away from infected people, as well as to encourage individuals to be vaccinated, 2) encouraging people infected with Covid-19 variants to self-isolate at home or join quarantine centers and encouraging severe cases go to hospitals and in the last control we use medical and psychological treatment to increase the immunity of people infected with different variants and reduce the number of people in hospitals and in isolation centers. We use the principle of the Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically using Matlab. Therefore, the results obtained confirm the performance of the optimization strategy.