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?