Vaccination’s Role in Combating the Omicron Variant Outbreak in Thailand: An Optimal Control Approach

Abstract

COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number , and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines and the infection rate will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak.

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

“…A new model must be used, one in which there are two variants are present, i.e., there are two types of infections, one caused by an α, β, γ, and δ variant of the COVID-19 coronavirus and another caused by the ω variant. A recent study by Lamwong et al [45] studied the efficiency of vaccines for COVID-19 in Thailand. It was found that a 10% increase of vaccination rates would cause a 10% increase of the basic reproduction number.…”

“…The basic reproduction number (R 0 ) represents the average number of secondary infections produced by an infected individual in a susceptible host population [45]. In an epidemiological model, if R 0 > 1, the disease will spread and may cause an epidemic, when R 0 < 1, an epidemic can be controlled.…”

“…Lamwong et al [45] studied the efficiency of vaccines for COVID-19 in Thailand. It was found that a 10% increase of vaccination rates would cause a 10% increase of the basic reproduction number.…”