PDF(Pubmed)
Abstract：
The COVID-19 pandemic, caused by SARS-CoV-2, disproportionately affected certain segments of society, particularly the elderly population (which suffered the brunt of the burden of the pandemic in terms of severity of the disease, hospitalization, and death). This study presents a generalized multigroup model, with m heterogeneous sub-populations, to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States. Rigorous analysis of the model for the homogeneous case (i.e., the model with m = 1) reveal that its disease-free equilibrium is globally-asymptotically stable for two special cases (with perfect vaccine efficacy or negligible disease-induced mortality) whenever the associated reproduction number is less than one. The model has a unique and globally-asymptotically stable endemic equilibrium, for special a case, when the associated reproduction threshold exceeds one. The homogeneous model was fitted using the observed cumulative mortality data for the United States during three distinct waves (Waves A (October 17, 2020 to April 5, 2021), B (July 9, 2021 to November 7, 2021) and C (January 1, 2022 to May 7, 2022)) chosen to align with time periods when the Alpha, Delta and Omicron were, respectively, the predominant variants in the United States. The calibrated model was used to derive a theoretical expression for achieving vaccine-derived herd immunity (needed to eliminate the disease in the United States). It was shown that, using the one-group homogeneous model, vaccine-derived herd immunity is not attainable during Wave C of the pandemic in the United States, regardless of the coverage level of the fully-vaccinated individuals. Global sensitivity analysis was carried out to determine the parameters of the model that have the most influence on the disease dynamics and burden. These analyses reveal that control and mitigation strategies that may be very effective during one wave may not be so very effective during the other wave or waves. However, strategies that target asymptomatic and pre-symptomatic infectious individuals are shown to be consistently effective across all waves. To study the impact of the disproportionate effect of COVID-19 on the elderly population, we considered the heterogeneous model for the case where the total population is subdivided into the sub-populations of individuals under 65 years of age and those that are 65 and older. The resulting two-group heterogeneous model, which was also fitted using the cumulative mortality data for wave C, was also rigorously analysed. Unlike for the case of the one-group model, it was shown, for the two-group model, that vaccine-derived herd immunity can indeed be achieved during Wave C of the pandemic if at least 61% of the populace is fully vaccinated. Thus, this study shows that adding age heterogeneity into a SARS-CoV-2 vaccination model with homogeneous mixing significantly reduces the level of vaccination coverage needed to achieve vaccine-derived herd immunity (specifically, for the heterogeneous model, herd-immunity can be attained during Wave C if a moderate proportion of susceptible individuals are fully vaccinated). The consequence of this result is that vaccination models for SARS-CoV-2 that do not explicitly account for age heterogeneity may be overestimating the level of vaccine-derived herd immunity threshold needed to eliminate the SARS-CoV-2 pandemic.
摘要：
COVID-19大流行，由SARS-CoV-2引起的，不成比例地影响了社会的某些阶层，特别是老年人(就疾病的严重程度而言，他们首当其冲地承受着大流行的负担，住院治疗,和死亡）。本研究提出了一个广义的多组模型，具有m个异质子种群，评估年龄异质性和疫苗接种对美国SARS-CoV-2大流行传播动态和控制的人群水平影响。对同质情况下的模型进行严格分析(即，m=1）的模型表明，每当相关的繁殖数小于1时，对于两个特殊情况（具有完美的疫苗效力或可忽略的疾病引起的死亡率），其无病平衡在全球范围内渐近稳定。该模型具有独特的全局渐近稳定的地方性均衡，对于特殊情况，当相关的再现阈值超过1时。使用美国在三个不同波期间观察到的累积死亡率数据拟合了均质模型(波A(2020年10月17日至2021年4月5日)，B（2021年7月9日至2021年11月7日）和C（2022年1月1日至2022年5月7日）选择与Alpha，Delta和Omicron是，分别,在美国的主要变体。使用校准的模型来推导用于实现疫苗衍生的群体免疫(在美国消除疾病所需)的理论表达。事实证明，使用一组齐次模型，在美国大流行的C波期间，疫苗衍生的群体免疫是无法实现的，无论完全接种疫苗的个人的覆盖率如何。进行了全局敏感性分析，以确定对疾病动态和负担影响最大的模型参数。这些分析表明，在一个波浪中可能非常有效的控制和缓解策略在另一个波浪中可能不是那么有效。然而,针对无症状和症状前感染个体的策略在所有波中始终有效.为了研究COVID-19对老年人群的不成比例影响，我们考虑了将总人口细分为65岁以下个体和65岁及以上个体的亚群体的异质模型.由此产生的两组异构模型，这也是用C波的累积死亡率数据拟合的，也进行了严格的分析。与单组模型的情况不同，它被证明，对于两组模型，如果至少61%的民众完全接种疫苗，疫苗衍生的群体免疫确实可以在大流行的C波期间实现。因此，这项研究表明，在具有均匀混合的SARS-CoV-2疫苗接种模型中添加年龄异质性可显着降低实现疫苗衍生的群体免疫所需的疫苗接种覆盖率（特别是，对于异构模型，如果适度比例的易感个体完全接种疫苗，则可以在C波期间获得群体免疫）。该结果的结果是，未明确说明年龄异质性的SARS-CoV-2疫苗接种模型可能高估了消除SARS-CoV-2大流行所需的疫苗衍生的群体免疫阈值的水平。
