Mathematical modeling and analysis of the impact of booster vaccination on COVID-19 eradication

In last two decades, people battled with three coronaviruses, namely Severe Acute Respiratory Syndrome (SARS) in November 2002; Middle East Respiratory Syndrome (MERS) in 2012 and finally the devastating SARS-CoV-2 infection or COVID-19 pandemic in December, 2019. Though the pandemic is now under control, we need to know whether it is completely eradicated or not. For this purpose, we have formulated a mathematical model incorporating three doses of corona vaccine and studied the impact of these vaccines on the disease dynamics. In our study, we have sought the conditions for eradication of the virus from the environment. To understand the consistency of the model, we have studied first its positivity and boundedness. Then we have carried out its steady-state analysis. The stability of the COVID-free equilibrium (CFE) and COVID-endemic equilibrium (CEE) points has been analyzed with the help of the basic reproduction number [Formula: see text], which is derived by the next-generation matrix approach. Further, this model has been validated by real data reported from India and estimated model parameters. Most effective model parameters are found by sensitivity analysis. Our findings show that first and second doses of COVID vaccines are not sufficient for eradication of the disease from the population, but the third (or booster) dose is able to control the disease if no comorbidity is considered.