用数学模型分析非典型肺炎预防和隔离措施的有效性

利用时滞常微分方程建立数学模型，研究在无任何预防和隔离措施的假想情况下非典型肺炎传染和发展的终极状态．通过对模型的讨论发现，在无任何预防和隔离措施的情况下，当非典疫情自生自灭以后，感染非典型肺炎的总人数占总人口的比例z主要取决于基本传染数R，即每个“非典”患者在其整个病程中的平均传染人数．根据有关报道3，4]，非典型肺炎的基本传染数R在2．2至3．6之间．根据我们的模型分析，当R=2．2时，z值可达85％左右，而当R=3．6时，z值可达97％左右．而事实上由于采取了预防和隔离措施，以北京市为例，感染非典型肺炎的总人数只有几千人，不到其总人口的千分之一．这充分说明了有关非典的预防和隔离措施的有效性．

Analysis of the Efficiency of the Preventing and Isolating Treatments of SARS Based on Mathematical Model

Based on a mathematical model of time-delayed differential equation, the asymptotic status of SARS infectivity when time tends to infinity was studied under the hypothetical condition of no preventing and isolating treatments. It is found that if no preventing and isolating treatments were taken the total number of people infected by SARS at the end of the epidemic was mainly determined by the basic reproductive number R. According to relevant reports 3,4], R ranges from 2.2 to 3.6 for SARS. The analysis of our model indicated that if no preventing and isolating treatments were taken, the total number of people infected by SARS at the end of the epidemic would reach 84% of the population when R = 2.2 and 97% whenR= 3.6. But the fact is not so. Take Beijing as an example, the total number of people infected by SARS is only several thousands and less than 0.1% of the population. This implies the efficiency of the preventing and isolating treatments of SARS.