Abstract
We present a restricted infection rate inverse binomial-based approach to better predict COVID-19 cases after a family gathering. The traditional inverse binomial (IB) model is inappropriate to match the reality of COVID-19, because the collected data contradicts the model’s requirement that variance should be larger than the expected value. Our version of an IB model is more appropriate, as it can accommodate all potential data scenarios in which the variance is smaller, equal, or larger than the mean. This is unlike the usual IB, which accommodates only the scenario in which the variance is more than the mean. Therefore, we propose a refined version of an IB model to be able to accommodate all potential data scenarios. The application of the approach is based on a restricted infectivity rate and methodology on COVID-19 data, which exhibit 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 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. Cluster 2, with a larger number of primary cases, exhibits smaller variance than the expected cases with a correlation of 79%, implying that the number of primary and secondary cases do increase or decrease together. Cluster 2 disqualifies the traditional IB model and requires its refined version. The 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 advantages of the proposed approach include the model’s ability to estimate the community’s health system memory, as future policies might reduce COVID’s spread. In our approach, the current hazard level to be infected with COVID-19 and the odds of not contracting COVID-19 among the primary in comparison to the secondary groups are estimable and interpretable.
Highlights
Background and motivationCOVID-19 is the third-leading cause of death in 2020 in the USA, Belgium, France, Sweden, and the UK, behind only heart disease and cancer
The odds for being safe after the family gathering is À ð1À yÞðtÀ 1Þ 1 y among the heterogeneously resistant participants as they identified by the infection rate restricted inverse binomial (IRRIB) model
The COVID-19 pandemic is a challenge to healthcare professionals, policy makers, epidemiologists and biostatisticians who try to model data and make successful predictions, and to the general public who faithfully adhere to recommendations such as social distancing, face covering, and utilizing good and frequent sanitizing practices
Summary
COVID-19 is the third-leading cause of death in 2020 in the USA, Belgium, France, Sweden, and the UK, behind only heart disease and cancer (www.kff.org). This research question is answered in the second part of this article For this purpose, new concepts of infectivity that restricted IB modeling processes are defined, and they are utilized to derive analytic expressions with an intention to better predict the future COVID-19 infection rates and cases. The odds for being safe after the family gathering is À ð1À yÞðtÀ 1Þ 1 y among the heterogeneously resistant participants as they identified by the infection rate restricted inverse binomial (IRRIB) model. Otherwise (that is, with a family gathering in which the attendees have heterogeneous resistance to COVID-19), the involvement of τ > 1 is a necessity in modeling to predict future COVID-19 cases. The odds for a safe situation in the IRRIB process (synonymous to a situation in which the family gathering involves attendees having heterogeneous resistance to COVID-19) against contracting COVID-19 is "(. (family gathering consists of attendees having heterogeneous resistance to COVID-19) sfififififififif ifififififififififififififififififififififif ifififi (family gathering consists of attendees having heterogeneous resistance to COVID-19)
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