Abstract
We introduce a novel n-stage vaccination model and corresponding system of differential equations that stratify a population according to their vaccination status. The model is an extension of the classical SIR-type models commonly used for time-course simulations of infectious disease spread and allows for the mitigation effects of vaccination to be uncoupled from other factors, such as changes in social behavior and the prevalence of virus variants. We fit the model to the Virginia Department of Health data on new COVID-19 cases, hospitalizations, and deaths broken down by vaccination status. The model suggests that, from 23 January through 11 September, fully vaccinated individuals were 89.8% less likely to become infected with COVID-19 and that the B.1.617.2 (Delta) variant is 2.08 times more transmissible than previously circulating strains of COVID-19. We project the model trajectories into the future to predict the impact of booster shots.
Highlights
In December 2019, a novel and highly-contagious coronavirus SARS-CoV-2 was identified in Wuhan, China
We used data points starting on 23 January and ending on 2 October and used linear interpolation to fill in missing data
We introduced a novel n-stage vaccination model (1) that stratifies a population according to their vaccination status
Summary
In December 2019, a novel and highly-contagious coronavirus SARS-CoV-2 was identified in Wuhan, China. After the Emergency Use Authorization of effective vaccines in the United States at the end of 2020 (Pfizer-BioNTech 11 December 2020; Moderna, 18 December 2020; Johnson & Johnson, 27 February 2021), the response focused on vaccination drives and awareness campaigns While these efforts have averted the worst-case forecast scenarios, COVID-19 continues to spread widely due in part to the more transmissible B.1.617.2 (Delta) variant, which became the dominant COVID-19 strain in the United States in July 2021 [2]. More recent research has focused on aspects of pharmaceutical interventions, such as comparing COVID-19 vaccination strategies (e.g., which segment of society to vaccinate first) and post-vaccination re-opening scenarios [15,16,17,18] While these and other studies incorporate vaccination into their modeling frameworks, time-course differential equation models have not been widely used to assess the realworld efficacy of vaccination itself. Studies on vaccine efficacy have been limited to controlled clinical trials [19,20,21] and analysis of data aggregates [22,23,24]
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