SIR模型对北京市SARS疫情流行规律的拟合研究

Research on fitting of SIR model on prevalence of SARS in Beijing city

目的 探讨SARS在人群中的传播规律 ,研究预防措施对疾病传播的影响 ,为预防的控制SARS提供科学依据。方法 根据北京市SARS原始数据和易感者、传染者及消除者 (SIR)模型方程组 ,计算出易感者、传染者及消除者人数 ,并求出传染率、消除比及阈值等具有流行病学意义的参数。结果 对上述三类人群数量进行拟合 ,预测值与实际值相符合 ,差异无显著性。估计 4月2 1日的易感者 (密切接触者和一般接触者 )人数为 81 4 70人 ,传染率r为 4 .0 31× 1 0 -5,消除比γ为 3.1 5 0 ,阈值 ρ为 781 4 5。 结论 SIR回归模型对SARS传播的拟合效果好 ,可用于理论上探讨预防措施对SARS发病及传播规律影响的研究。 4月 2 1日后采取的预防措施及时有效 。

Objective To investigate the transmission rules of SARS, to study the effects of corresponding prevention measures, and to provide evidence for the prevention and control. Methods The number of susceptible, infected and removed in Beijing city has been calculated using susceptible infected removed (SIR) model, all parameters with epidemiological meaning including transmission rate, removal ratio and threshold value have been estimated. Results The model got very good fitting results. The predicted values accorded with the true values well and there was no significant difference between them. The total susceptible which include close contact and general contact estimated on April 21st was 81 470, transmission rater r was 4.031×10 -5 , removal ratio γ was 3.150, the threshold value ρ was 78 145. Conclusions SIR model can be used to study the influence of preventive measures to the occurrence and transmission rules of SARS in theory. Public health efforts have had significant impact on reducing the size of the epidemic.