Quantifying the effects of vaccines and a booster vaccine dose on the dynamics of COVID-19 in the United States

The coronavirus disease 2019 (COVID-19) pandemic continues to have a devastating impact on health systems and economies across the globe, with the USA among the worse impacted nations. Implementing public health measures in tandem with effective vaccination strategies is instrumental in halting the transmission of the virus and curtailing the pandemic. Currently, the Food and Drug Administration (FDA) has authorized the use of the Pfizer-BioNTech, Moderna and the Johnson and Johnson vaccines to prevent COVID-19. With these vaccines having varying efficacy and waning effect against major circulating strains, their impact on the incidence of COVID-19 is relevant. Here, we deploy a deterministic mathematical model to investigate the impact of each type of vaccine and the administration of booster doses on the incidence of cases driven by the major circulating variants in the US (Omicron and Delta) and predict the future trend of the disease dynamics. Applying a modified SEIR model, we determined the reproduction number and showed that having a reproduction number less than unity did not guarantee the disease was under control because of the backward bifurcation phenomenon hidden in the model. The fitting and numerical simulation of the framework indicated that during a wave where the vaccination peaks, the reproduction number reduced by 44% and the peak size decreased by more than 71% compared to the preceding wave. We showed that in the absence of booster shots, the peak size for the wave caused by the delta variant could have been approximately 1.5 times the magnitude observed. We observed that a booster shot with the mRNA vaccines conferred superior protection than that of the Johnson and Johnson vaccine. Additionally, the estimated transmission rate based on our model is three times higher with the Omicron variant in circulation and predicts a spike of approximately 1 billion new cases by the end of January 2022. However, the magnitude of this peak could decrease to around 400 thousand if 10% of the eligible population for booster doses receive these doses early. This finding suggests that early vaccine administration and booster doses can effectively mitigate the pandemic.