Is large-scale vaccination sufficient for controlling the Covid-19 pandemic with uncertainties? A model-based study

A massive vaccination program against SARS-CoV-2 infection started at the beginning of 2021. Studies show that vaccinated people are subject to reinfection, and there is uncertainty in the rate of immunity loss, the force of infection, recovery rate, vaccine efficacy. Here we study a six-dimensional stochastic epidemic model with vaccine-induced immunity loss to demonstrate the effect of vaccination in controlling the Covid-19 epidemic. It is shown that the disease persists for a long time if the stochastic basic reproduction number (SBRN) is greater than unity. We have also proved a sufficient condition for disease eradication. Our analysis shows that the disease cannot persist if R 0V ext <1. Noticeably, this condition may not hold if the infectivity increases or/and the vaccine-induced immunity loss increases. A case study was done using the Indian Covid-19 data to estimate the model parameters and the noise intensities. It is revealed that the mean extinction time increases with the increasing rate of immunity loss and force of infection. A nontrivial observation is that mass vaccination cannot eradicate the disease if the vaccine-induced immunity loss is higher than 23 %. The case is almost similar if the infectivity is also high. It implies that the infection will last long unless a long-lasting vaccine candidate appears or a low infectious variant replaces the highly contagious variant.