School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, China.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China.
Comput Biol Med. 2023 Oct;165:107431. doi: 10.1016/j.compbiomed.2023.107431. Epub 2023 Sep 1.
Since the end of 2019 the COVID-19 repeatedly surges with most countries/territories experiencing multiple waves, and mechanism-based epidemic models played important roles in understanding the transmission mechanism of multiple epidemic waves. However, capturing temporal changes of the transmissibility of COVID-19 during the multiple waves keeps ill-posed problem for traditional mechanism-based epidemic compartment models, because that the transmission rate is usually assumed to be specific piecewise functions and more parameters are added to the model once multiple epidemic waves involved, which poses a huge challenge to parameter estimation. Meanwhile, data-driven deep neural networks fail to discover the driving factors of repeated outbreaks and lack interpretability. In this study, aiming at developing a data-driven method to project time-dependent parameters but also merging the advantage of mechanism-based models, we propose a transmission dynamics informed neural network (TDINN) by encoding the SEIRD compartment model into deep neural networks. We show that the proposed TDINN algorithm performs very well when fitting the COVID-19 epidemic data with multiple waves, where the epidemics in the United States, Italy, South Africa, and Kenya, and several outbreaks the Omicron variant in China are taken as examples. In addition, the numerical simulation shows that the trained TDINN can also perform as a predictive model to capture the future development of COVID-19 epidemic. We find that the transmission rate inferred by the TDINN frequently fluctuates, and a feedback loop between the epidemic shifting and the changes of transmissibility drives the occurrence of multiple waves. We observe a long response delay to the implementation of control interventions in the four countries, while the decline of the transmission rate in the outbreaks in China usually happens once the implementation of control interventions. The further simulation show that 17 days' delay of the response to the implementation of control interventions lead to a roughly four-fold increase in daily reported cases in one epidemic wave in Italy, which suggest that a rapid response to policies that strengthen control interventions can be effective in flattening the epidemic curve or avoiding subsequent epidemic waves. We observe that the transmission rate in the outbreaks in China is already decreasing before enhancing control interventions, providing the evidence that the increasing of the epidemics can drive self-conscious behavioural changes to protect against infections.
自 2019 年底以来，COVID-19 疫情反复出现，大多数国家/地区都经历了多波疫情，基于机制的流行模型在理解多波疫情传播机制方面发挥了重要作用。然而，由于传统的基于机制的流行 compartment 模型通常假设传播率是特定的分段函数，并且一旦涉及多波疫情，模型中就会添加更多参数，因此捕捉 COVID-19 在多波疫情期间的传染性的时间变化仍然是一个未解决的问题。同时，数据驱动的深度神经网络无法发现疫情反复爆发的驱动因素，缺乏可解释性。在这项研究中，为了开发一种数据驱动的方法来预测时变参数，同时结合基于机制模型的优势，我们提出了一种通过将 SEIRD compartment 模型编码到深度神经网络中的传输动力学信息神经网络（TDINN）。我们表明，所提出的 TDINN 算法在拟合具有多波疫情的 COVID-19 疫情数据时表现非常出色，其中以美国、意大利、南非和肯尼亚的疫情以及中国的几次奥密克戎变体疫情为例。此外，数值模拟表明，训练有素的 TDINN 还可以作为预测模型来捕捉 COVID-19 疫情的未来发展。我们发现，由 TDINN 推断出的传播率经常波动，疫情转移和传染性变化之间的反馈循环驱动了多波疫情的发生。我们观察到在四个国家/地区实施控制干预措施的响应延迟较长，而在中国疫情爆发时，传播率的下降通常发生在实施控制干预措施之后。进一步的模拟表明，意大利一次疫情中控制干预措施实施延迟 17 天，每日报告病例数将增加约四倍，这表明对加强控制干预措施的政策迅速做出反应可以有效控制疫情曲线或避免后续疫情。我们观察到，在中国的疫情爆发之前，传播率已经在下降，这表明疫情的增加可以促使人们自觉改变行为以防止感染。
