A Compartmental Model for Assessing Effects of COVID-19 Vaccination in Thailand

Abstract

A dynamical model for COVID-19 spread relating to non-pharmaceutical interventions and vaccination is mathematically generated by adding a gradual vaccination compartment for the susceptible population and considering only a symptomatic infectious stage. In our model, there are seven compartments dividing a given population into susceptible <img src=image/17628733_01.gif>, vaccinated <img src=image/17628733_02.gif>, exposed <img src=image/17628733_03.gif>, infected <img src=image/17628733_04.gif>, quarantined <img src=image/17628733_05.gif>, recovered <img src=image/17628733_06.gif> and death <img src=image/17628733_07.gif> groups, respectively. Then, theoretically analysis is given by investigating the COVID-19 free and endemic equilibrium points, and computing the vaccination reproduction number of this model denoted as <img src=image/17628733_08.gif> using the next generation matrix. If <img src=image/17628733_09.gif>, then the COVID-19 transmission increases exponentially and depends on vaccine efficacy. On the other hand, if <img src=image/17628733_10.gif>, then there occurs the COVID-19 disease eradication. The risk from infection can be importantly reduced whenever the intake of COVID-19 vaccines exceeds one dose. The numerical results reveal that the nonpharmaceutical ways and the administered COVID-19 vaccines can be effective against the current variants of COVID-19, and the additional efforts such as a third vaccine booster shot should be considered and implemented to greatly mitigate the risks of emerging variants of the COVID-19 virus. Moreover, combining different types of COVID-19 vaccines can be appeared as a possible way to give better protection against COVID-19 as well.