This article constructs a restricted infection rate inverse binomial-based approach to predict COVID-19 cases after a family gathering. The traditional inverse binomial (IB) model is unqualified to match the reality of COVID-19, because the data contradicts the model’s requirement that variance should be greater than expected value. A refined version of the IB model is a necessity to predict COVID-19 cases after family gatherings. Our refined version of an IB model is more appropriate and versatile, as it accommodates all potential data scenarios: equal, lesser, or greater variance than expected value.Application of the approach is based on a restricted infectivity rate and methodology on Fan et al.’s COVID-19 data, which exhibits two clusters of infectivity. Cluster 1 has a smaller number of primary cases and exhibits larger variance than the expected cases with a negative correlation of 28%, implying that the number of secondary cases is lesser when the number of primary cases increases and vice versa. The traditional inverse binomial (IB) model is appropriate for Cluster 1. The probability of contracting COVID-19 is estimated to be 0.13 among the primary, but is 0.75 among the secondary in Cluster 1, with a wider gap. Conversely, Cluster 2, exhibits smaller variance than the expected cases with a correlation of 79%, implying the number of primary and secondary cases increase or decrease together. Cluster 2 disqualifies the traditional IB model and demands its refined version. Probability of contracting COVID-19 is estimated to be 0.74 among the primary, but is 0.72 among the secondary in Cluster 2, with a narrower gap.The model’s ability to estimate the community’s health system memory for future policies to be developed is an asset of this approach. The current hazard level to be infected with COVID-19 among the primary and secondary groups are estimable and interpretable.

中文翻译：

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预测未知的对感染性具有同质或异质性的COVID-19病例

本文构建了一个基于有限感染率逆二项式的方法来预测家庭聚集后的COVID-19病例。传统的逆二项式（IB）模型不符合COVID-19的实际条件，因为数据与模型要求方差应大于期望值相矛盾。IB模型的完善版本对于在家庭聚会后预测COVID-19病例很有必要。我们完善的IB模型版本更合适，更通用，因为它可以适应所有潜在的数据场景：与期望值相等，更小或更大的方差。该方法的应用是基于Fan等人的受限感染率和方法论。的COVID-19数据，显示出两个传染性簇。聚类1的主要案例数量较少，并且与预期案例相比具有更大的方差，具有28％的负相关性，这意味着当主要案例数量增加时，次要案例的数量会减少，反之亦然。传统的逆二项式（IB）模型适用于集群1。在集群1中，收缩COVID-19的概率在主要人群中估计为0.13，而在次要人群中为0.75，两者之间的差距更大。相反，聚类2的方差小于预期案例，相关性为79％，这意味着主要案例和次要案例的数量一起增加或减少。集群2取消了传统IB模型的资格，并要求其改进版本。在群集2中，签约COVID-19的概率在主要节点中估计为0.74，但在次要节点中为0.72。该模型能够估计社区的卫生系统记忆以制定未来的政策，这是该方法的优势。在主要和次要人群中，目前感染COVID-19的危险程度是可以估算和解释的。