Modeling COVID-19 Breakthrough Infections in a Vaccinated Population

Abstract

The consequences of the COVID-19 pandemic that originated in Wuhan, China in 2019 are still being felt globally. At the onset of the pandemic, countries had several measures in place to prevent the spread of the virus. The development and availability of COVID-19 vaccines turned out to be one of the most effective tools for containing the pandemic, especially in developed countries. This paper considers a model of COVID-19 breakthrough infections, which are cases where individuals become infected with COVID-19 despite being fully vaccinated. The model proposed is a type of the SIR model with a compartment accounting for vaccinated individuals and is governed by a system of differential equations. We compute the basic reproduction number of the model and use it to analyze the equilibria for both local and global stability. Further, we use numerical simulations of the model to understand the factors that contribute to breakthrough infections such as vaccination rates, vaccine efficacy, and virus transmission dynamics.