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

A massive vaccination programme against COVID-19 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 and 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 R-0V(S) > 1 holds. We have also proved a sufficient condition for disease eradication. Our analysis shows that the disease cannot persist if R-0V(ext) <1. However, this latter condition may not hold if the infectivity increases and/or the vaccine-induced immunity loss increases. Indian and Italian COVID-19 data are used to demonstrate various dynamical behaviours of the system and disease persistence. A non-trivial observation is that mass vaccination cannot eradicate the disease if the vaccine-induced immunity loss is high. Disease eradication is also challenging with the ongoing immunization process if the infectivity of the virus is also high. These results decipher that the infection will last long unless a long-lasting vaccine candidate appears or a low infectious variant replaces the highly contagious COVID-19 variant.