A Mathematical Model of U.S. COVID-19 Deaths, Incidence and Quarantine Adjusted Herd Immunity by Age
Abstract In January 2021, a steep decline in U.S. COVID-19 deaths and case reports were noted, well before herd immunity or vaccinations would have been expected make an impact. This model predicts COVID-19 deaths and infections based on three insights. First, mortality rates differ significantly by age. Second, heterogeneous social mixing by age during quarantine may result in older adults (higher risk) to have more effectively quarantined conferring lower incidence relative to younger adults (lower risk and disproportionate essential frontline work). Third, deaths and Infection Fatality Rates may more reliably predict incidence relative to reported cases by removing uncertainty introduced from asymptomatic disease, testing availability, and false results. Age stratified IFR and deaths through December 5 were used to projected deaths (99% significance, P-value .002). Sensitivities for IFR, immune durability, and vaccinations were also modeled. By end 2020, 42% of the U.S. population had immunity differing significantly by age with 25-44-year-olds near 80%. A “critical mass” of immunity in these ages segments conferred herd immunity to other age groups. Herd immunity exists in the context of historic social distancing (quarantine). A significant percent of high-risk individuals remains susceptible and may facilitate another wave if social distancing restrictions are lifted prior to vaccination. Vaccine administrations through mid-February contributed a nominal amount to declining deaths.