Modeling the effects of preventive measures and vaccination on the COVID-19 spread in Benin Republic with optimal control

Abstract

Coronavirus disease (COVID-19) onset in December 2019 is a contagious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since, the spread of the virus and mortality due to COVID-19 have continued to increase daily leading to a pandemic. In absence of approved medicine and vaccines, many countries imposed policies such as social distancing, mask wearing, hand washing, airport screening, quarantine and others. But rapidly, they were confronted with the high economic and social cost resulting from those policies. Many vaccines have been proposed but their efficiency is still controversial. Now, governments and scholars search for how manage with preventives measures policies and vaccination campaigns to stop the COVID-19 spread. This work studied the effects of these different strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contribution in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without respect of preventives measures. The optimal control analysis was carried out using the Pontryagin's maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings revealed that the optimal implementation of preventive measures reduce highly the number of infected individuals but zero infection was not achieved in the population. That was obtained with the optimal implementation of vaccination campaigns which reduce the number of infected individuals. But the optimal and combined implementation of the two interventions performed better with less costs than the two singular implementations.

Keywords: COVID-19; Mathematical modeling; Optimal control; Preventive measures; Vaccination.

Fig. 1

The diagram of the COVID-19 model.

Fig. 2

Evolution of numbers of individuals in the compartments I (Fig. 2(a)), J (Fig. 2(b)) and D (Fig. 2(c)) with optimal control on preventive measures.

Fig. 3

Evolution of numbers of individuals in the compartments I (Fig. 3(a)), J (Fig. 3(b)) and D (Fig. 3(c)) with optimal control on vaccination.

Fig. 4

Evolution of the numbers of individuals in the compartments I (Fig. 4(a)), J (Fig. 4(b)), D (Fig. 4(c)), with optimal control on the effort vaccination and preventive measures.