[论文解读] Neural Network aided quarantine control model estimation of COVID spread in Wuhan, China

Raj Dandekar, George Barbastathis|arXiv (Cornell University)|Mar 18, 2020

COVID-19 epidemiological studies参考文献 14被引用 37

一句话总结

该论文使用神经网络增强的SIR模型来量化武汉封控对COVID-19传播的影响，显示R(t)在一个月内从>1降至<1，并在继续封控下预测持续控制。

ABSTRACT

In a move described as unprecedented in public health history, starting 24 January 2020, China imposed quarantine and isolation restrictions in Wuhan, a city of more than 10 million people. This raised the question: is mass quarantine and isolation effective as a social tool in addition to its scientific use as a medical tool? In an effort to address this question, using a epidemiological model driven approach augmented by machine learning, we show that the quarantine and isolation measures implemented in Wuhan brought down the effective reproduction number R(t) of the CoVID-19 spread from R(t) &gt; 1 to R(t) &lt;1 within a month after the imposition of quarantine control measures in Wuhan, China. This ultimately resulted in a stagnation phase in the infected case count in Wuhan. Our results indicate that the strict public health policies implemented in Wuhan may have played a crucial role in halting down the spread of infection and such measures should potentially be implemented in other highly affected countries such as South Korea, Italy and Iran to curtail spread of the disease. Finally, our forecasting results predict a stagnation in the quarantine control measures implemented in Wuhan towards the end of March 2020; this would lead to a subsequent stagnation in the effective reproduction number at R(t) &lt;1. We warn that immediate relaxation of the quarantine measures in Wuhan may lead to a relapse in the infection spread and a subsequent increase in the effective reproduction number to R(t) &gt;1. Thus, it may be wise to relax quarantine measures after sufficient time has elapsed, during which maximum of the quarantined/isolated individuals are recovered.

研究动机与目标

• 使用自2020年1月24日及以后数据，量化武汉封禁与隔离措施对COVID-19传播的影响。
• 开发一个神经网络辅助的流行病学模型，以学习随时间变化的封控强度Q(t)及其对R(t)的影响。
• 使用经典的SEIR/SIR框架比较有无封控的情景，并评估对1个月时间视界的预测能力。

提出的方法

• 用一个对输入(S, I, R, T)进行运算的两层神经网络表示的随时间变化的封控强度Q(t)来增强SIR模型。
• 定义 dS/dt = -β SI/N, dI/dt = β SI/N - γ I - Q(t) I, dR/dt = γ I, dT/dt = Q(t) I, 其中 R(t) = β/(γ+Q(t)).
• 通过最小化使对数变换后的 I(t) 和 R(t) 与数据 (I_data, R_data) 相匹配的损失来训练增强系统。
• 在学习 Q(t) 的同时，估计最优的 β、γ 和神经网络权重 W，以再现观测到的感染动态和封控效果。

实验结果

研究问题

• RQ1 在早期疫情爆发期间，随时间变化的封控强度如何影响武汉的有效再生产数R(t)？
• RQ2 神经网络增强的SIR模型是否能够再现感染病例的观测性停滞，并量化封控在阻止传播中的作用？
• RQ3 随着封控措施随时间推移的发展，Q(t)和R(t)的预测轨迹是什么，对放松时机有何影响？

主要发现

• 若无封控，经典的SEIR/SIR模型无法再现2020年1月24日之后感染病例的观测性停滞。
• 有封控时，模型捕捉到感染高峰时的停滞；在峰值时约60万人被隔离/封控，Q(t)在一个月内从约0.5上升到约0.7。
• R(t)在封控实施一个月内从约1.5下降至低于1。
• 一个月预测显示在放松封控时，Q(t)在约0.75附近停滞，R(t)仍<1，但放松可能带来复发风险，如果已经康复的个体还未完全不会传染。
• 该研究强调在充分恢复后逐步放松的潜在需要，并指出局限性，如未建模无症状传播或封控与非封控人群之间的接触。