中国湖北省 COVID-19 空间扩散的引力与自回归分析
Gravitational and Autoregressive Analysis Spatial Diffusion of COVID-19 in Hubei Province, China
AI总结：
本文利用局部引力模型和空间自回归分析研究 COVID-19 从武汉向湖北扩散的规律，发现幂律衰减引力模型拟合良好，并揭示城市规模、距离及隔离措施对疫情扩散的重要影响。
摘要：
传染病的空间扩散在地理学中遵循距离衰减规律，但在不同时空条件下，不同的扩散过程可能由不同的数学函数建模。本文致力于对源自武汉市并向湖北省扩散的 COVID-19 空间扩散模式进行建模。方法包括引力分析和空间自回归分析。局部引力模型由异速标度和全局引力模型推导而来，然后利用观测数据和线性回归估计局部引力模型的参数。主要结果如下。基于幂律衰减的局部引力模型能够有效描述湖北省 COVID-19 的扩散模式和过程，而基于负指数衰减的引力模型对观测数据的拟合优度不令人满意。进一步地，模型对数据的拟合优度随时间推移整体变得越来越好，规模弹性系数先增大后减小，距离衰减指数先减小后增大。此外，模型中空间自回归系数的显著性较低，置信水平低于 80%。可以得出以下结论。（1）湖北省 COVID-19 的空间扩散具有长程效应，城市规模以及该城市与武汉的距离影响确诊病例总数。（2）在早期阶段，武汉直接传播是湖北省 COVID-19 空间扩散的主要过程，区域之间的水平传播不显著。（3）中国政府为阻断 COVID-19 传播所采取的空间隔离措施效果明显。本研究表明，在预防和控制传染病时应考虑引力的作用。
英文摘要：
The spatial diffusion of epidemic disease follows distance decay law in geography, but different diffusion processes may be modeled by different mathematical functions under different spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province. The methods include gravity and spatial auto-regression analyses. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and linear regression. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observation data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of gravity should be taken into account to prevent and control epidemic disease.
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