The efficacy of vaccines in the context of COVID-19 and its variants: Role of Spatio-temporal boundary

Roy, D.; Chakravortty, D.; Basu, S.

The vaccine efficacy is a crucial determining factor in choosing a vaccine candidate for human use. When the choices of vaccines are many, the decision-making becomes difficult. General public resorts to the media and news, which talks about efficacies of various vaccines as observed for COVID-19. In this paper, for the first time, a concise mathematical framework for analyzing the efficacy of vaccines is introduced based on the standard definition of vaccine efficacy. The framework is then generalized to incorporate multi-variants. Finally, we introduce the idea of combined efficacy to characterize a vaccine efficacy as obtained from various clinical trials carried out across the world for Covid-19. We show that the efficacy reported by vaccine manufacturers from clinical trial data need not always directly translate to percentage efficacy. The efficacy of a vaccine is inherently a spatio-temporal statistical measure that characterizes a vaccine, which depends on the geographical location, the sample size, and the time of the clinical trials. Here, the dependence of efficacy on spatio-temporal parameters is expounded in detail, using hypothetical clinical trials conducted for different regions at different time intervals using real-world data.