北京2003年SARS疫情的数值模拟  

Numerical simulation of SARS epidemic in Beijing in 2003

作　　者：刘双[1] 王天辉[2] 

机构地区：[1]鞍山师范学院数学系,辽宁鞍山114005 [2]营口职业技术学院,辽宁营口115000

出　　处：《生物数学学报》2010年第4期740-744,共5页Journal of Biomathematics

摘　　要：在文[1]的基础上,进一步考虑了每天从外地输入北京的SARS病人数和处于传染期的病人在发病后被收治的概率.利用Gauss-Newton最优化方法对相关参数进行了估计,结果表明,初始病人数为3.5人,医院外第一、二阶段的传染率分别为0.5655(1/天)、0.1425(1/天),医院内第一、二阶段的传染率分别为0.0470(1/天)、0.00(1/天),病人发病后八天内被医院收治,期间每天被医院收治的概率从第一天的0.1632严格递减至第八天的0.0776.累计病人数、累计出院与死亡人数之和的模拟值与实际统计值的相对误差都小于1%.On the basis of reference[1],this paper furtherly considerates the number of SARS patients which come from outside Beijing and the probability of the patients in the infectious stage being accepted after outbreak.The parameters were estimated in the model by Gauss-Newton optimization method.The parameters estimation shows that the initial numbers of patients in infectious period equal to 3.5,the infection rates outside hospitals during the first and second stage equal to 0.5655（1/day） and 0.1425（1/day）,respectively,0.0470（1/day） and 0.00（1/day）,inside hospitals;patients were accepted by hospitals within 8 days after becoming bad.The probability of being accepted every day strictly decreased from 0.1632 in the 1^（st） day to 0.0776 in the 8^（th） day.The relative error between the simulated and observed values of the total patient numbers is less than 1%,and so is that of the sum of numbers of recovered and died patients in hospital.

关 键 词：SARS 差分方程 Gauss-Newton最优化方法 参数估计 

分 类 号：O175.7[理学—数学] O242.1[理学—基础数学]