Department of Mathematics and Statistics, The University of Ottawa, Ottawa, ON, Canada.
Department of Mathematics, Ilam University, Ilam, Iran.
Sci Rep. 2021 Nov 26;11(1):22970. doi: 10.1038/s41598-021-00083-2.
Several vaccines with different efficacies and effectivenesses are currently being distributed across the world to control the COVID-19 pandemic. Having enough doses from the most efficient vaccines in a short time is not possible for all countries. Hence, policymakers may propose using various combinations of available vaccines to control the pandemic with vaccine-induced herd immunity by vaccinating a fraction of the population. The classic vaccine-induced herd-immunity threshold suggests that we can stop spreading the disease by vaccinating a fraction of the population. However, that classic threshold is defined only for a single vaccine and may be invalid and biased when we have multi-vaccine strategies for a disease or multiple variants, potentially leading policymakers to suboptimal vaccine-allocation policies. Here, we determine which combination of multiple vaccines may lead to herd immunity. We show that simplifying the problem and considering the vaccination of the population as a single-vaccine strategy whose effectiveness is the sample mean of all effectivenesses would not be ideal, because many multi-vaccine strategies with a smaller herd-immunity threshold can be proposed. We show that the herd-immunity threshold may vary due to changes in vaccine-uptake proportions. Moreover, we propose methods to determine the optimal combination of multiple vaccines in order to achieve herd immunity and apply our results to the issue of multiple variants. In addition, we determine a condition for reaching herd immunity in the presence of new emerging variants of concern. We show by example that new variants could influence our estimation of the vaccination reproduction number. It follows that the herd-immunity threshold must be updated not only when multi-vaccine strategies are used but also when multiple variants coexist in the population.
目前，全球正在分发几种具有不同功效的疫苗，以控制 COVID-19 大流行。并非所有国家都能在短时间内获得最有效的疫苗的足够剂量。因此，政策制定者可能会提议使用各种现有疫苗组合，通过为部分人群接种疫苗来控制大流行，从而实现疫苗诱导的群体免疫。经典的疫苗诱导群体免疫阈值表明，我们可以通过为部分人群接种疫苗来阻止疾病的传播。然而，该经典阈值仅针对单一疫苗定义，当我们针对疾病或多种变体有多种疫苗策略时，可能无效且存在偏差，从而使政策制定者采取次优的疫苗分配政策。在这里，我们确定了多种疫苗的哪种组合可能会导致群体免疫。我们表明，将问题简化并将人群接种疫苗视为单一疫苗策略，其有效性是所有有效性的样本平均值，这并不理想，因为可以提出许多具有较小群体免疫阈值的多疫苗策略。我们表明，由于疫苗接种比例的变化，群体免疫阈值可能会发生变化。此外，我们提出了确定多种疫苗最佳组合以实现群体免疫的方法，并将我们的结果应用于多种变体的问题。此外，我们确定了在存在新出现的令人担忧的变体时达到群体免疫的条件。我们举例表明，新变体可能会影响我们对疫苗繁殖数的估计。因此，不仅在使用多疫苗策略时，而且在人群中同时存在多种变体时，都必须更新群体免疫阈值。
