Infection by SARS‐CoV‐2 with alternate frequencies of mRNA vaccine boosting

One of the most consequential unknowns of the COVID‐19 pandemic is the frequency at which vaccine boosting provides sufficient protection from infection. We quantified the statistical likelihood of breakthrough infections over time following different boosting schedules with messenger RNA (mRNA)‐1273 (Moderna) and BNT162b2 (Pfizer‐BioNTech). We integrated anti‐Spike IgG antibody optical densities with profiles of the waning of antibodies and corresponding probabilities of infection associated with coronavirus endemic transmission. Projecting antibody levels over time given boosting every 6 months, 1, 1.5, 2, or 3 years yielded respective probabilities of fending off infection over a 6‐year span of >93%, 75%, 55%, 40%, and 24% (mRNA‐1273) and >89%, 69%, 49%, 36%, and 23% (BNT162b2). Delaying the administration of updated boosters has bleak repercussions. It increases the probability of individual infection by SARS‐CoV‐2, and correspondingly, ongoing disease spread, prevalence, morbidity, hospitalization, and mortality. Instituting regular, population‐wide booster vaccination updated to predominant variants has the potential to substantially forestall—and with global, widespread uptake, eliminate—COVID‐19.


| INTRODUCTION
The unprecedented development of efficacious vaccines against SARS-CoV-2 was hailed as a triumph in the global effort to control the ongoing COVID-19 pandemic. Vaccines were shown to provide short-term protection from infection and major adverse health outcomes of hospitalization and death. [1][2][3][4] However, protection from infection by SARS-CoV-2 wanes over the short term, 5 and breakthrough infections are increasingly frequent, 6,7 raising the question of how often vaccine boosters should be administered. The FDA and the CDC have been working to keep booster recommendations current in the face of serial, somewhat unpredictable variant-driven waves of infection. 8 As COVID-19 becomes an endemic disease, regular boosting of vaccination is likely advisable. 9 Consequently, rigorous prediction of the immunity over time that would be conferred by candidate boosting schedules against SARS-CoV-2 infection is essential for personal and public health decision-making.
Such predictions regarding the ability of regular boosting to fend off infections have major implications worldwide. 10,11 Short-term longitudinal studies of SARS-CoV-2 neutralizing antibodies in vaccinated and boosted individuals [12][13][14] indicate that antibody-mediated protection against infection wanes after vaccination, 15 and after vaccine boosting. 16 Long-term longitudinal reinfection data have not been collected for SARS-CoV-2 and insufficient information has been gathered from direct studies of protection against infection by vaccination and boosting to identify the consequent long-term protection conferred by candidate boosting schedules. However, data on antibody responses, their waning, and corresponding probabilities of infection have been collected for a diversity of closely related coronaviruses. [17][18][19][20][21][22] Here, we quantify the effect of boosting by pairing antibody responses and their waning consequent to booster vaccination with corresponding infection probabilities. The aim of this study is to assess these probabilities of infection over the long term to evaluate alternate serial boosting schedules.

| Study design
We expanded on a comparative evolutionary framework for inference of infection probability associated with antibody level after natural infection. 23 This framework enabled us to estimate the typical peak antibody response to vaccination with mRNA-1273 and BNT162b2, relative to natural infection. We obtained published empirical antibody waning profiles following vaccination with mRNA-1273 and BNT162b2 and supplemented them with subsequent waning dynamics inferred from an ancestral and descendent states analysis incorporating observed antibody waning of the six human-infecting coronaviruses HCoV-OC43, HCoV-NL63, and HCoV-229E, SARS-CoV-1, SARS-CoV-2, and MERS. We then used ancestral and descendent states analysis to infer parameters for logistic regression models of the endemic probabilities of infection based on antibody level. Projecting waning and boosting over 6 years at intervals ranging from every 6 months to every 3 years, we quantified probabilities of boosted breakthrough infection.

| Phylogenetic tree topologies
Phylogenetic tree topologies for the relationships of SARS-CoV-2 and the endemic human-infecting coronaviruses were obtained from Townsend et al. 23 These tree topologies are based on data from 58 Alphacoronavirus, 105 Betacoronavirus, 11 Deltacoronavirus, and 3 Gammacoronavirus that were analyzed by multiple maximum-likelihood analyses of concatenated DNA sequence alignments of the S, M, and ORF1b genes. Resulting topologies were found to be robust to alternative maximum-likelihood search algorithms, 24,25 to alternative divergence time estimation approaches, 24,[26][27][28] and to a potential history of recombination. 29

| Waning antibody data
To obtain data that would provide relative peak antibody levels comparing BNT162b2 with natural infection and mRNA-1273 occurring at a known time relative to antibody measurement, we conducted literature searches using the PubMed and Google Scholar databases. Searches were conducted between July 1, 2021 and October 24, 2022, using combinations of the terms "SARS-CoV-2," "BNT162b2," "mRNA-1273," "antibodies," "antibody response," "ELISA," "IgG," "longitudinal," "optical density," "naive," "seropositive," "natural infection," or "convalescent." There were no language restrictions imposed. Studies were included when they reported ELISA anti-S, anti-S1, or anti-RBD data that covered the peak antibody response for naive individuals vaccinated with mRNA-1273 or BNT162b2 compared to those with natural infection and no prior vaccination.
The relative peak antibody levels comparing mRNA-1273 and "SARS-CoV-2," "BNT162b2," "mRNA-1273," "antibodies," "antibody response," "ELISA," "IgG," "longitudinal," "optical density," "naive," "booster," or "second dose" without language restrictions. Inclusion criteria necessitated that studies reported ELISA anti-S, anti-S1, or anti-RBD data that covered the peak antibody response for naive individuals vaccinated and subsequently boosted with mRNA-1273 or vaccinated and subsequently boosted with BNT162b2. Additionally, optical density measures of antibody levels subsequent to the first vaccination series and after boosting had to be measured by the same lab using the same assay to ensure standardized measurements.
This antibody-waning data set was then supplemented by further analysis of a data set assembled by Townsend et al. 23 on waning antibody levels following natural infection by SARS-CoV-2 and its closest human-infecting relatives. To supplement the natural infection data gathered by Townsend et al. 23 we incorporated data assembled by Townsend et al. 9 that included alternative SARS-CoV-2 data from two studies 30,31 that met the criteria of having sufficient ELISA optical density data on anti-S1 IgG antibody levels beyond the anti-S1 IgG antibody level data set provided by Townsend et al. 23 These natural infection studies used a consistent antibody type (Euroimmun S1) and provided longitudinal sampling, thereby ensuring that our comparative phylogenetic analyses were conducted on a common scale of immunological measurement. 32 We used the six comparative data sets assembled in Townsend et al. 9 to assess the robustness of our findings to data selection. Data set 1 comprised anti-S1 data from a population sample of 1797 individuals extending over 125 days after diagnosis of infection by SARS-CoV-2, 33 nine individuals (five male and four female; age: 27-54 years) infected by MERS-CoV with symptoms ranging from asymptomatic to severe, monitored up to 18 months, 17 and putative endemic coronavirus anti-S1 IgG antibody waning data from our linear model relating anti-N and anti-S1 IgG that included 10 adult males aged 27-75 years who were assayed for antibody response to infection by HCoV-OC43, HCoV-NL63, and HCoV-229E over 28 years spanning two periods: 1984-1997 and 2003-2020. 18 Data sets 2 and 3 included alternate SARS-CoV-2 data from two sources: (Data set 2) 264 individuals over 28 weeks whose positive status was validated by two or more assays in addition to the Euroimmun anti-S1 assay, 30  October, 2022 using as terms combinations of "BNT162b2," "mRNA-1273," "antibodies," "antibody response," "coronavirus," "ELISA," "IgG," "immunity," "immune response," "longitudinal monitoring," "optical density," "Euroimmun," "S protein," "Spike protein," "reinfection," "serological," and "titer."

| Waning antibody profiles and baselines
We constructed profiles of SARS-CoV-2 anti-S1 IgG antibody waning through time as in Townsend et al. 9 We For each virus, antibody waning was related to its probability of infection using logistic regression of daily probability of infection against antibody level, ( ) . Parameters a v (intercept) and b v (slope) for each endemic coronavirus v, dependent on g, the peaknormalized antibody level, were fit to data from Edridge et al. 18 analyzed as in Townsend et al. 9 We series. We then projected waning beginning at the product of ratios (1) and (3) for mRNA-1273, or at the product of (2) and (4)   For mRNA-1273, literature search yielded six studies meeting all inclusion criteria that reported peak antibody levels following the first series of mRNA-1273 vaccination in comparison to peak antibody levels following the first series of BNT162b2 (Table 1).
These studies ranged

| Estimation of long-term antibody waning rates
Projection of the waning antibody levels postpeak in response to natural infection by SARS-CoV-2 exhibited consistent estimates of half-life to baseline, ranging from 36 to 156 days between data sets (Supporting Information: Table 1).

| Risk of breakthrough infection associated with each boosting schedule
Results for each mRNA vaccine were highly similar. In the absence of  Figure 1A; BNT162b2: 87% with cessation of boosting to 77% with boosting every 3 years, Figure 1B). Annual boosting resulted in a substantial reduction in 6-year risk (to 25% for mRNA-1273, Figure 1A; to 31% for BNT162b2, Figure 1B). Boosting every 6 months induced the highest level of protection, with a risk of breakthrough infection over 6 years that is less than 7% for mRNA-1273, compared with 11% for BNT162b2. These results were consistent regardless of SARS-CoV-2 waning antibody data set used (Table 2). Alternate compositions of the antibody-waning data sets for related viruses provided consistent results with respect to relative decreases in probability of no breakthrough infection at the close of these intervals, but differed modestly in the scale of risk associated with each booster schedule (Supporting Information: Figure 1).