Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand

Abstract

The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point’s stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin’s maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another.