Estimating COVID-19 Infections, Hospitalizations, and Deaths Following the US Vaccination Campaigns During the Pandemic

This decision analytic modeling study uses a simulation model to evaluate the association of US COVID-19 vaccination campaigns with infections, hospitalizations, and deaths.

21% (95% CI: 11-36%) 26,27 . This evasion rate was implemented as a reduction of immune protection for individuals recovered from the original strain or the Alpha variant, corresponding to an average transmission probability of 0.21×0.109= 0.0229 per contact. We further assumed that recovery from infection due to the Gamma or Delta variant provides protection against all variants in the model, preventing reinfection for at least one year.

Infection outcomes
We assumed that asymptomatic and mild symptomatic cases recover from infection without hospitalization. A proportion of those with severe disease were hospitalized within 2-5 days of symptom onset 28,29 and were therefore removed from the transmission chain. We also assumed that all symptomatic cases who were not hospitalized self-isolated within 24 hours of symptom onset, and reduced their number of daily contacts by an additional 72% (eTable 1). Intensive care unit (ICU) and non-ICU hospitalization rates were parameterized (eTable 2) by clinical and epidemiological data stratified by age and comorbidities [30][31][32] . Infection with Alpha variant was associated with 64% higher risk of death 9,10 , and infections with Gamma or Delta variants were assigned the case fatality of the original strain.

Vaccination
We implemented a two-dose vaccination campaign with a sequential prioritization of: (i) healthcare workers (5% of the total population) 35 , adults with comorbidities, and those aged 65 and older; and (ii) other individuals aged 16-64 36,37 . Based on vaccine uptake data, we assigned 60% probability of vaccination for individuals aged 40-64 years and 40% vaccination probability for individuals aged 16-39 years 38 . The minimum age-eligibility for vaccination was 16 years before May 13, 2021 after which children aged 12 to 15 years became eligible for vaccination. We used reported daily vaccine doses administered since the start of vaccination to parameterize a rolling 7-day average of vaccine distribution per 100,000 population 39 .
We specified Pfizer-BioNTech vaccines with an interval of 21 days between the first and second doses 40 . This interval was 28 days for Moderna vaccines 41 . We parameterized the model with published estimates of vaccine efficacy following each dose of Pfizer-BioNTech and Moderna vaccines against infection, symptomatic disease, and severe disease caused by the original strain 1,42 . The mean efficacies, reported in eTable 3, were implemented in the model as a reduction of transmission probability (for efficacy against infection), reduction in probability of developing symptomatic disease, and reduction of severe illness if symptomatic disease occurred.

Data sources
The overall demographic characteristics and temporal distribution of individuals receiving COVID-19 vaccines was obtained from the CDC data repository 39 . Daily COVID-19 infections (i.e., confirmed by a test), and deaths (reported as associated with COVID-19) were obtained from New York Times Github repository 43 . Daily new COVID-19 hospital admissions were retrieved from the HealthGov data repository 44 .

Model implementation
Assuming 10% pre-existing immunity generated by the original strain prior to October 2020 56,57 , we simulated the model with a population of 100,000 individuals from October 1, 2020 to December 1, 2021. To incorporate the age distribution of pre-existing immunity in the population, we ran the model with only the original strain in the absence of vaccination and determined the infection rates in different age groups when the overall attack rate reached 10%. The distribution of this immunity was used to parameterize the initial population at the start of simulations.
On April 2, the guidelines by the US Centers for Disease Control and Prevention indicated a minimal risk for fully vaccinated individuals to travel and engage in certain social activities while taking COVID-19 precautions 58 . We therefore allowed vaccinated individuals to return to prepandemic behaviour 14 days after the second dose of vaccine from April 3, 2021.
During the calibration process (in the presence of only the original strain of SARS-CoV-2), we used a 50% lower rate of contacts (compared to pre-pandemic normal behaviour) and determined the transmission probability of 0.109 per contact in the pre-symptomatic stage of infection. Transmissibility during other stages of infection was adjusted according to their infectivity relative to the pre-symptomatic stage. The transmission probability obtained during the calibration corresponds to an effective reproduction number of 1.17 in early October 2020 6 , accounting for the effect of NPIs. After the calibration, the transmission probability of the original strain remained fixed and the age-specific contact rates were adjusted throughout the simulations (in all scenarios with and without vaccination) to implicitly account for the change in various NPIs implemented in the US and fit the model to observed incidence data. The model was implemented in Julia, which is an open-source, high-performance, dynamic programming language that allows rapid analysis of computationally intensive problems, such as agent-based modelling. Simulations were averaged over 500 independent Monte-Carlo realizations, and 95% credible intervals derived using a bias-corrected and accelerated bootstrap method. The simulation codes are available at: https://github.com/thomasvilches/multiple_strains/tree/rapid_vaccination