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

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.

2019年12月出现了一种新型冠状病毒（新冠病毒肺炎，COVID - 19），引发了一场大流行，给世界各个角落带来了前所未有的公共卫生和经济负担。虽然最初对新冠病毒的控制主要集中在使用基本的公共卫生措施（主要基于非药物干预措施，如检疫、隔离、社交距离、佩戴口罩和社区封锁），但2020年12月有三种安全且高效的疫苗（由阿斯利康公司、莫德纳公司和辉瑞公司研发）被批准用于人类。我们提出了一个新的数学模型，用于评估这些疫苗在减轻新冠病毒肺炎负担方面对人群层面的影响。该模型根据人们在公共场合是否习惯佩戴口罩将总人口分为两个亚组。由此产生的多组模型是一个非线性微分方程的确定性系统，利用美国新冠病毒肺炎第三波疫情的累计死亡数据进行拟合和参数设定。严格推导了相关无病平衡点的渐近稳定性条件以及疫苗衍生的群体免疫阈值的表达式。该模型的数值模拟表明，佩戴口罩群体中初始个体比例的大小，以及非佩戴口罩群体（以及佩戴口罩群体中不放弃佩戴口罩习惯的人）行为的积极改变，在有效遏制美国的新冠病毒肺炎大流行方面起着至关重要的作用。这项研究进一步表明，在美国使用辉瑞或莫德纳疫苗实现疫苗衍生的群体免疫（消除新冠病毒肺炎所需）的前景相当乐观。特别是，我们的研究表明，如果至少60%的人口完全接种疫苗，美国就可以实现群体免疫。此外，如果疫苗接种计划辅以适度提高依从性水平（相对于其基线依从性）的非药物干预措施，2021年在美国消除大流行的前景将显著提高。该研究还表明，虽然针对新冠病毒肺炎的自然免疫和疫苗衍生免疫的减弱只会导致大流行负担和预计消除时间的轻微增加，但将疫苗的治疗益处纳入模型后，大流行的负担和消除时间大幅减少。