Toward Achieving a Vaccine-Derived Herd Immunity Threshold for COVID-19 in the U.S.

Abstract

A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that inflicted unprecedented public health and economic burden in all nooks and corners of the world. Although the control of COVID-19 largely focused on the use of basic public health measures (primarily based on using non-pharmaceutical interventions, such as quarantine, isolation, social-distancing, face mask usage, and community lockdowns) initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc., and Pfizer Inc.), were approved for use in humans in December 2020. We present a new mathematical model for assessing the population-level impact of these vaccines on curtailing the burden of COVID-19. The model stratifies the total population into two subgroups, based on whether or not they habitually wear face mask in public. The resulting multigroup model, which takes the form of a deterministic system of nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative mortality data for the third wave of the COVID-19 pandemic in the United States. Conditions for the asymptotic stability of the associated disease-free equilibrium, as well as an expression for the vaccine-derived herd immunity threshold, are rigorously derived. Numerical simulations of the model show that the size of the initial proportion of individuals in the mask-wearing group, together with positive change in behavior from the non-mask wearing group (as well as those in the mask-wearing group, who do not abandon their mask-wearing habit) play a crucial role in effectively curtailing the COVID-19 pandemic in the United States. This study further shows that the prospect of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in the year 2021 is significantly enhanced if the vaccination program is complemented with non-pharmaceutical interventions at moderate increased levels of compliance (in relation to their baseline compliance). The study further suggests that, while the waning of natural and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in the burden and time-to-elimination of the pandemic.

Dynamics of the Delta and Omicron variants of SARS-CoV-2 in the United States: the battle of supremacy in the presence of vaccination, mask usage and antiviral treatment

“…The model ( 7) is an extended version of numerous COVID-19 transmission models in the literature that consider the dynamics of multiple co-circulating variants, such as those in [46][47][48][49][50][51][52][53][54][55] by, inter alia, including:…”

Vaccination Schedule under Conditions of Limited Vaccine Production Rate

“…Research using models of this type was also presented in [25][26][27][28]. The models presented in [29,30] consider the effect induced by vaccination and continuous use of non-pharmaceutical interventions (NPI). Bubar et al [31] conducted a study using an age-stratified SEIR model to identify the age groups that should receive the highest priority in access to vaccination.…”

Optimal Control Applied to Vaccination and Testing Policies for COVID-19

“…The duration of immunity against COVID-19 is still an open research question. In the last year, several works have proposed different epidemic models, including a wide variety of immunity loss rates, which assume a duration of the immunity ranging from a few months to several years [30][31][32][33][34][35]. In this work, the sensitivity of the OCP to the immunity loss rate is analyzed, in which the duration of the immunity is assumed to be between 6 months and 3 years [36,37].…”