Predicting COVID-19 cases with unknown homogeneous or heterogeneous resistance to infectivity
Abstract
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.
Author Summary
Current statistical models are not able to accurately predict disease infection spread in the COVID-19 pandemic. We have applied a widely-used inverse binomial method to predict rates of infection after small gatherings, going from primary (original) cases to secondary (later) cases after family gatherings or social events, using the data from the Wuhan and Gansu provinces in China, where the virus first spread. The advantages of the proposed approach include that the model’s ability to estimate the community’s health system memory for future policies to be developed, as such policies might reduce COVID’s spread if not its control. In our approach, as demonstrated, the current hazard level of becoming infected with COVID-19 and the odds of contracting COVID-19 among the primary in comparison to the secondary groups are estimable and interpretable. We hope the proposed approach will be used in future epidemics.
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