Résumé
This study proposes a corona pandemic model that incorporates both reported and unreported cases of virus to be more realistic. In addition, it is advised to employ both preventive measures: vaccination and treatment and applied them at the simultaneously. The optimal controls were characterized with the maximum Pontryagin principle. Finally, the results of the numerical simulations demonstrate the utility of the proposed control mechanisms and this modeling. © 2023, SCIK Publishing Corporation. All rights reserved.
Résumé
In this paper, we propose a mathematical model of infection by infectious diseases, taking into account the division of the population according to the criteria of immunity. Our objective is to demonstrate the positive effect of this idea against the different epidemics. We have proposed two strategies to reduce the great human and material losses caused by these diseases, respectively awareness programs on the importance of the exercise of sport and a healthy food to increase human immunity, treatment and health care for people with low immunity. The Pontryagin maximum principle is applied to characterize the optimal controls, and the optimality system is solved using an iterative approach. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB. © 2022 the author(s).
Résumé
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).
Résumé
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. © 2022 the author(s).