Deo Vishal, Grover Gurprit
Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India.
Department of Statistics, Ramjas College, University of Delhi, Delhi, India.
Results Phys. 2021 May;24:104182. doi: 10.1016/j.rinp.2021.104182. Epub 2021 Apr 15.
In the absence of sufficient testing capacity for COVID-19, a substantial number of infecteds are expected to remain undetected. Since the undetected cases are not quarantined, they can be expected to transmit the infection at a much higher rate than their quarantined counterparts. That is, in the absence of extensive random testing, the actual prevalence and incidence of the SARS-CoV-2 infection can be significantly higher than that being reported. Thus, it is imperative that the information on the percentage of undetected (or unreported) cases be incorporated in the mechanism for estimating the key epidemiological parameters, like rate of transmission, rate of recovery, reproduction rate, , and hence, for forecasting the transmission dynamics of the epidemic. In this paper, we have developed a new dynamic version of the basic susceptible-infected-removed (SIR) compartmental model, called the susceptible-infected (quarantined/ free) - recovered- deceased [SI(Q/F)RD] model, to assimilate the impact of the time-varying proportion of undetected cases on the transmission dynamics of the epidemic. Further, we have presented a Dirichlet-Beta state-space formulation of the SI(Q/F)RD model for the estimation of its parameters using posterior realizations from the Gibbs sampling procedure. As a demonstration, the proposed methodology has been implemented to forecast the COVID-19 transmission in California and Florida. Results suggest significant amount of underreporting of cases in both states. Further, posterior estimates obtained from the state-space SI(Q/F)RD model show that average reproduction numbers associated with the undetected infectives [California: 1.464; Florida: 1.612] are substantially higher than those associated with the quarantined infectives [California: 0.497; Florida: 0.359]. The long-term forecasts of death counts show trends similar to those of the estimates of excess deaths for the comparison period post training data timeline.
在缺乏足够的新冠病毒检测能力的情况下，预计会有大量感染者未被发现。由于未被发现的病例没有被隔离，预计他们传播感染的速度会比被隔离的病例高得多。也就是说，在没有广泛随机检测的情况下，新冠病毒感染的实际流行率和发病率可能会显著高于报告的数字。因此，必须将未被发现（或未报告）病例的百分比信息纳入估计关键流行病学参数（如传播率、康复率、繁殖率等）的机制中，从而预测疫情的传播动态。在本文中，我们开发了一种新的动态版本的基本易感-感染-移除（SIR） compartmental模型，称为易感-感染（隔离/未隔离）-康复-死亡[SI(Q/F)RD]模型，以吸收未被发现病例的时变比例对疫情传播动态的影响。此外，我们提出了SI(Q/F)RD模型的狄利克雷-贝塔状态空间公式，用于使用吉布斯采样程序的后验实现来估计其参数。作为一个示范，已实施所提出的方法来预测加利福尼亚州和佛罗里达州的新冠病毒传播情况。结果表明，这两个州都存在大量病例漏报的情况。此外，从状态空间SI(Q/F)RD模型获得的后验估计表明，与未被发现的感染者相关的平均繁殖数[加利福尼亚州：1.464；佛罗里达州：1.612]大大高于与被隔离的感染者相关的平均繁殖数[加利福尼亚州：0.497；佛罗里达州：0.359]。死亡人数的长期预测显示出与训练数据时间线后比较期的超额死亡估计趋势相似的趋势。
