SARS疫情的标度性质及其物理意义

A Scaling Property of SARS Cases and Its Physical Implications

使用Zipf分布研究了2003年4月20日前后中国内地各省的SARS疫情,发现SARS病例数满足分段的幂律关系,其中不同的段分别相应于不同的传播方式。资料显示,4月20日前后北京地区处于非常特殊的状态,此时所采取的非常措施看来是十分必要的。

In the physics of complexity, the scaling law in the output of a system contains important information about the underlying mechanism which is responsible for the macroscopic behavior of the system. In the study on the scientific problems associated with the control of the Severe Acute Respiratory Syndrome (SARS) , the mechanism of SARS propagation is one of the important topics under discussion. To study the mechanism of SARS propagation, Zipf distribution (or rank-ordering analysis) is applied to describe the scaling property of SARS onsets around April 20,2003, for different provinces/municipalities/ autonomous regions in Chinese mainland, for comparison, number of SARS cases is normalized by the population of each province. Both cumulative total and daily increase as well as smoothed daily increase are considered in the analysis. Three power-law type frequency-case distributions can be observed from the rank-ordering analysis, corresponding to different types of SARS propagation mechanisms respectively. From the scaling laws, the propagation of SARS shows three typical mechanisms, namely migration, self-affection, and intermediate or mixed type. Analysis also shows that around April 20,20003, Beijing is in a very special state as remarked by its cumulative number of SARS cases much smaller than expected from the scaling of other provinces and the rate of increase much higher than expected from the scaling, which means that at the time Beijing is in a very unstable state; therefore, the quasi-emergency response of Beijing at that time is necessary, although not timely to much extent, to control the SARS propagation. The scaling law observed here can be used as a constraint of the physical models describing the dynamics of SARS propagation. The scaling analysis is also of help in answering the frequently asked questions as what will be the characteristic length of the quasi-emergencey state in Beijing? and what is the criteria that the SARS propagation has been under control and the quasi-emergencey state could be ended?