Mathematical Modeling of Vaccines That Prevent SARS-CoV-2 Transmission

Abstract

SARS-CoV-2 vaccine clinical trials assess efficacy against disease (VEDIS), the ability to block symptomatic COVID-19. They only partially discriminate whether VEDIS is mediated by preventing infection completely, which is defined as detection of virus in the airways (VESUSC), or by preventing symptoms despite infection (VESYMP). Vaccine efficacy against transmissibility given infection (VEINF), the decrease in secondary transmissions from infected vaccine recipients, is also not measured. Using mathematical modeling of data from King County Washington, we demonstrate that if the Moderna (mRNA-1273QS) and Pfizer-BioNTech (BNT162b2) vaccines, which demonstrated VEDIS > 90% in clinical trials, mediate VEDIS by VESUSC, then a limited fourth epidemic wave of infections with the highly infectious B.1.1.7 variant would have been predicted in spring 2021 assuming rapid vaccine roll out. If high VEDIS is explained by VESYMP, then high VEINF would have also been necessary to limit the extent of this fourth wave. Vaccines which completely protect against infection or secondary transmission also substantially lower the number of people who must be vaccinated before the herd immunity threshold is reached. The limited extent of the fourth wave suggests that the vaccines have either high VESUSC or both high VESYMP and high VEINF against B.1.1.7. Finally, using a separate intra-host mathematical model of viral kinetics, we demonstrate that a 0.6 log vaccine-mediated reduction in average peak viral load might be sufficient to achieve 50% VEINF, which suggests that human challenge studies with a relatively low number of infected participants could be employed to estimate all three vaccine efficacy metrics.

Improving vaccination coverage and offering vaccine to all school-age children allowed uninterrupted in-person schooling in King County, WA: Modeling analysis

“…We adapted a deterministic compartment model, developed and iteratively improved by our team, which describes the epidemic dynamics in King County, Washington, USA [ 28 , 30 – 32 ]. Our model ( Figure 1A and Figure S1 ) stratifies the population by age (0–19 years, 20–49 years, 50–69 years, and 70+ years), infection status (susceptible, exposed, asymptomatic, pre-symptomatic, symptomatic mild, symptomatic severe), clinical status (undiagnosed, diagnosed, hospitalized), immunity (susceptible, vaccinated, recovered from natural infection), and infecting strain (original, Alpha, Delta).…”

“…We implemented reactive social distancing (SD) allowing numbers of cases and hospitalizations to fluctuate due to the community response to the epidemic [ 36 ]. We used intermediate range of contact reduction, more than pre-pandemic levels but less than a full lockdown [ 28 , 30 – 32 ].…”

Vaccination, Immunity and Breakthrough: Quantitative Effects in Individual Immune Responses Illustrated by a Simple Kinetic Model

“…The completeness of protection given by vaccination is also an important factor for achieving herd immunity. For reliable protection of a whole population, the number of people who must be vaccinated increases with decreasing efficacy of vaccines, which can be clearly demonstrated by mathematical modeling [15]. Simulations show that a vaccine efficacy of more than 70% is required for achieving herd immunity, but vaccination of 66% of a population is sufficient if the vaccine efficacy is above 90% [16].…”

A mathematical model of the within-host kinetics of SARS-CoV-2 neutralizing antibodies following COVID-19 vaccination

“…While many useful models focus on modeling epidemiological dynamics and answering questions about population-level effects of interventions such as vaccination and treatment ( c.f. Diagne et al, 2021 , Swan et al, 2021 ), our interest is in addressing questions about protective immunity within a vaccinated individual. Some excellent within-host mathematical models have been developed to focus on a variety of questions about response to virus, treatment, and vaccination.…”