National Center of Mathematics and Interdisciplinary Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.
Capital University of Economics and Business, Beijing, 100070, China.
BMC Infect Dis. 2023 Oct 11;23(1):679. doi: 10.1186/s12879-023-08667-1.
The emergency of new COVID-19 variants over the past three years posed a serious challenge to the public health. Cities in China implemented mass daily RT-PCR tests by pooling strategies. However, a random delay exists between an infection and its first positive RT-PCR test. It is valuable for disease control to know the delay pattern and daily infection incidences reconstructed from RT-PCR test observations.
We formulated the convolution model between daily incidences and positive RT-PCR test counts as a linear inverse problem with positivity restrictions. Consequently, the Richard-Lucy deconvolution algorithm was used to reconstruct COVID-19 incidences from daily PCR tests. A real-time deconvolution was further developed based on the same mathematical principle. The method was applied to an Omicron epidemic data set of a bar outbreak in Beijing and another in Wuxi in June 2022. We estimated the delay function by maximizing likelihood via an E-M algorithm.
The delay function of the bar-outbreak in 2022 differs from that reported in 2020. Its mode was shortened to 4 days by one day. A 95% confidence interval of the mean delay is [4.43,5.55] as evaluated by bootstrap. In addition, the deconvolved infection incidences successfully detected two associated infection events after the bar was closed. The application of the real-time deconvolution to the Wuxi data identified all explosive incidence increases. The results revealed the progression of the two COVID-19 outbreaks and provided new insights for prevention and control strategies, especially for the role of mass daily RT-PCR testing.
The proposed deconvolution method is generally applicable to other infectious diseases if the delay model can be assumed to be approximately valid. To ensure a fair reconstruction of daily infection incidences, the delay function should be estimated in a similar context in terms of virus variant and test protocol. Both the delay estimate from the E-M algorithm and the incidences resulted from deconvolution are valuable for epidemic prevention and control. The real-time feedback is particularly useful during the epidemic's acute phase because it can help the local disease control authorities modify the control measures more promptly and precisely.
在过去三年中，新出现的 COVID-19 变体的紧急情况对公共卫生构成了严重挑战。中国的城市通过汇集策略实施了大规模的日常 RT-PCR 检测。然而，从感染到首次阳性 RT-PCR 检测之间存在随机延迟。了解从 RT-PCR 检测观察结果中重建的延迟模式和每日感染发生率对于疾病控制很有价值。
我们将每日发病率和阳性 RT-PCR 检测计数之间的卷积模型表示为具有阳性限制的线性反问题。因此，Richard-Lucy 反卷积算法被用于从每日 PCR 检测中重建 COVID-19 发病率。基于相同的数学原理，进一步开发了实时反卷积。该方法应用于 2022 年北京酒吧疫情和无锡另一疫情的奥密克戎疫情数据集。我们通过 EM 算法最大化似然来估计延迟函数。
2022 年酒吧疫情的延迟函数与 2020 年报告的不同。其模式通过一天缩短到 4 天。通过 bootstrap 评估，平均延迟的 95%置信区间为[4.43,5.55]。此外，反卷积后的感染发病率成功检测到酒吧关闭后的两次关联感染事件。实时反卷积在无锡数据中的应用识别出所有爆炸性发病率增加。结果揭示了这两次 COVID-19 疫情的进展，并为预防和控制策略提供了新的见解，特别是对大规模日常 RT-PCR 检测的作用。
如果可以假设延迟模型大致有效，则所提出的反卷积方法通常适用于其他传染病。为了确保每日感染发病率的公平重建，应根据病毒变体和检测方案在类似的情况下估计延迟函数。来自 EM 算法的延迟估计和反卷积产生的发病率都对疫情防控有价值。实时反馈在疫情急性阶段特别有用，因为它可以帮助当地疾病控制当局更及时、更精确地修改控制措施。
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