基于反应扩散方程研究新型冠状病毒肺炎在武汉早期传播特征

本文基于SEIR空间反应扩散模型，研究了新型冠状病毒肺炎在武汉市早期的传播情况．基于中国疾控中心及武汉市卫健委发表文献中公开的数据，提出反应扩散方程的最小二乘法格式，并使用最小二乘法对传染率进行了参数估计，获得了模型参数的最优估计值．在此基础上，基于模型对2019年12月8日至2020年1月5日之间的染病者、潜伏者进行空间传播模拟，模拟显示疾病会从单点暴发发展到多点染病，而且固定空间位置的染病者数量会随着扩散而增大．进一步对扩散速率和传染率进行了敏感性分析，揭示了累计染病者数量会随着传染率和扩散速率的增大而增大，对传染率的敏感性大于其对扩散速率的敏感性．因此，对于突发传染病，及时切断传染源和有效降低传染率是防控传染病进一步蔓延的有效举措，比如早发现早隔离，居家隔离，增加社交距离和外出戴口罩都可以有效降低染病者数量．

The Early Transmission Characteristics of Corona Virus Disease 2019 Based on the Reaction Diffusion Equation in Wuhan

The paper researches the early transmission characteristics of Corona Virus Disease 2019 in Wuhan based on the SEIR (Susceptible-Exposed-Infectious-Removed) spatial reaction diffusion model. In terms of the open data published by China CDC and Wuhan Health Committee, the least square formula of reaction diffusion equation is proposed, then the parameter estimation of the infection rate is calculated by the least square method and the optimal values of model parameters are obtained. The model simulates the spatial transmission of the infected and potential patients from December 8, 2019 to January 5, 2020 showing that the disease will develop from single point outbreak to multi-point infection. In the meantime, the number of patients in fixed space will increase with the spread. Furthermore, the sensitivity analysis of diffusion rate and infection rate reveals that the cumulative number of the infected will increase with the increase of infection rate and diffusion rate, the sensitivity of infection rate is greater than that of diffusion rate. Therefore, for the emergent infectious diseases, timely source cutting-off of infection and effective reduction of infection rate are good measures to the prevention and control to further spread of infectious diseases. For example, the measures of early discovery, early isolation and home isolation, social distance increasing and masks wearing in the outside can effectively reduce the number of the infected.