Short-term forecasts and long-term mitigation evaluations for the COVID-19 epidemic in Hubei Province, China 湖北省2019冠状病毒疾病疫情的短期预报和长期减灾评估

Short-term forecasts and long-term mitigation evaluations for the COVID-19 epidemic in Hubei Province, China 湖北省2019冠状病毒疾病疫情的短期预报和长期减灾评估

原文链接：https://www.sciencedirect.com/science/article/pii/S2468042720300312

Abstract

摘要
As an emerging infectious disease, the 2019 coronavirus disease (COVID-19) has developed into a global pandemic. During the initial spreading of the virus in China, we demonstrated the ensemble Kalman filter performed well as a short-term predictor of the daily cases reported in Wuhan City. Second, we used an individual-level network-based model to reconstruct the epidemic dynamics in Hubei Province and examine the effectiveness of non-pharmaceutical interventions on the epidemic spreading with various scenarios. Our simulation results show that without continued control measures, the epidemic in Hubei Province could have become persistent. Only by continuing to decrease the infection rate through 1) protective measures and 2) social distancing can the actual epidemic trajectory that happened in Hubei Province be reconstructed in simulation. Finally, we simulate the COVID-19 transmission with non-Markovian processes and show how these models produce different epidemic trajectories, compared to those obtained with Markov processes. Since recent studies show that COVID-19 epidemiological parameters do not follow exponential distributions leading to Markov processes, future works need to focus on non-Markovian models to better capture the COVID-19 spreading trajectories. In addition, shortening the infectious period via early case identification and isolation can slow the epidemic spreading significantly.

作为一个新兴传染病，2019年的冠状病毒病(2019冠状病毒疾病)已经发展成为一个全球性的流行病。在病毒最初在中国传播期间，我们演示了集合卡尔曼滤波器作为武汉市每日报告病例的短期预报器表现良好。其次，采用基于个体层面的网络模型重建湖北省疫情动态，并在不同情景下检验非药物干预对疫情传播的有效性。我们的模拟结果表明，如果没有持续的控制措施，湖北省的疫情可能会持续下去。只有通过1)保护措施和2)社会疏远继续降低感染率，才能在模拟中重建湖北省实际疫情的发展轨迹。最后，我们用非马尔可夫过程模拟了2019冠状病毒疾病的传播，并展示了这些模型如何产生不同的流行病轨迹，与马尔可夫过程模型相比。 由于最近的研究表明，2019冠状病毒疾病的流行病学参数不服从马尔可夫过程的指数分布，未来的工作需要集中在非马尔可夫模型，以更好地捕捉2019冠状病毒疾病的扩散轨迹。此外，通过早期病例识别和隔离，缩短传染期，可以显著减缓疫情的蔓延。

Conclusion

In this work, the ensemble Kalman filter is used to make short-term predictions of the COVID-19 cases in Wuhan City, which resulted in accurate forecasts of daily case reports. The model is able to predict daily cases and the epidemic peak. Knowing the daily cases from forecasts three days in advance allows for the proper resource allocation. The ensemble Kalman filter also allows parameter estimation, which is extremely useful for modeling purposes.

本文利用集合卡尔曼滤波器对武汉市的2019冠状病毒疾病进行了短期预报，实现了对每日病例报告的准确预报。该模型能够预测日病例数和疫情高峰期。通过提前三天了解预测中的每日情况，可以进行适当的资源分配。集合卡尔曼滤波器还允许参数估计，这是非常有用的建模目的。

From an epidemiological modeling perspective, we simulate the epidemic spreading in Wuhan city based on non-Markovian processes, and show that different distributions with the same mean infectious period can lead to inconsistency in terms of epidemic dynamics. Since most current network-based approaches are based on Markov processes, in which epidemiological parameters are assumed to follow exponential distributions, non-Markovian process-based models need to be further explored to better predict the COVID-19 spreading. Our results show that reducing the infectious period via measures such as early case identification and isolation can reduce the epidemic size significantly.

从流行病学建模的角度，利用非马尔可夫过程模拟了武汉市的传染病传播过程，结果表明，不同的平均传染期分布会导致传染病传播动力学的不一致性。由于目前大多数基于网络的方法是基于马尔可夫过程，其中流行病学参数假定服从指数分布，非马尔可夫过程模型需要进一步探索，以更好地预测2019冠状病毒疾病扩散。我们的结果表明，通过早期病例识别和隔离等措施缩短传染期，可以显著降低疫情规模。

In the long-term perspective, we test and confirm the effectiveness of non-pharmaceutical interventions on the containment of the epidemic dynamics by performing GEMF stochastic simulations. The daily cases of the COVID-19 epidemic in Hubei Province peaked at over 15,000 on February 12th and became almost zero in mid-March (Xinhua, 2020). Our simulation results indicate that the containment of this highly contagious disease was achieved by stringent control measures by the Chinese government. Without continued and aggressive control measures, the epidemic in Hubei Province would have become more severe. Only with combined implementation of enhanced protective measures and social distancing measures, the epidemic dynamics would peak at around mid-February and approximate the actual epidemic trajectory in March. This can be an important message for countries going through the exponential growth of the epidemic in the current days.

从长远来看，我们通过施行 GEMF 随机模拟测试和确认非药物干预对遏制流行病动态的有效性。2月12日，湖北省2019冠状病毒疾病疫情达到高峰，每天超过15000例，到3月中旬几乎为零(新华社，2020年)。我们的模拟结果表明，中国政府采取了严格的控制措施，遏制了这种高度的接触传染病。如果没有持续和积极的控制措施，湖北省的疫情会变得更加严重。只有联合执行加强保护措施和社会疏远措施，疫情动态才会在2月中旬左右达到高峰，并在3月份接近实际疫情轨迹。对于目前正在经历艾滋病指数增长的国家来说，这可能是一个重要的信息。

Appendix

A1 Data collection

The population size of each city in Hubei Province is obtained from the Hubei Statistical Yearbook (Hubei Provincial Bureau of Statistics, 2020). We collected Baidu Migration data (https://qianxi.baidu.com/) for the 17 cities in the Hubei Province from January 1st to January 29th, 2020. The daily Baidu migration data contain two types of data. First type: the data include the immigration index and emigration index of each city, which are linearly related to the human traffic volume moving in and out of individual cities. Second type: for each city i, the data also contain the composition of city i’s incoming flow, namely the fraction of flows coming from every other city j to city i (flow from city j to i divided by the total flow coming into city i). Similarly, the data contain the fraction of flows going out of city i to city m (flow from city i to m divided by the total flow going out of city i).
湖北省各城市人口规模取自《湖北省统计年鉴》(湖北省统计局，2020年)。从2020年1月1日到1月29日，我们收集了湖北省17个城市的百度迁移数据( https://qianxi.baidu.com/)。每日百度迁移数据包含两种类型的数据。第一类: 数据包括每个城市的移民指数和移民指数，它们与进出城市的人流量呈线性关系。第二种类型: 对于每个城市 i，数据还包含城市 i 的流入流的组成，即来自每个其他城市 j 到城市 i 的流量的比例(从城市 j 到 i 的流量除以进入城市 i 的总流量)。类似地，数据包含从城市 i 流向城市 m 的流量的比例(从城市 i 流向 m 除以从城市 i 流出的总流量)。
Based on the fact that around 5 million people have moved out of Wuhan before the city lockdown on January 23rd (Zhu et al., 2020), we obtain the number of people that traveled between the cities using the following approach. First, we estimate value of , which equals 5 million divided by the sum of Wuhan’s emigration indexes from January 1st to January 23rd. Then, we can calculate the population flow moving in or out of each individual city by times the immigration or emigration index. In addition, the population flow multiplied by the flow fraction going to or coming from a specific city gives us the number of daily travelers to or from a particular individual city to another.
基于在1月23日武汉封锁之前，大约有500万人已经迁出武汉这一事实(朱等人，2020) ，我们使用以下方法获得了在城市之间往返的人数。首先，我们估计 α 值，它等于500万除以武汉1月1日至1月23日移民指数之和。然后，我们可以用移民指数的 α 乘以每个城市的人口迁入迁出量。此外，人口流动乘以进出某个特定城市的人口流动比例，就得出了每天往返于某个特定城市的旅客人数。