应用随机网络对SARS在北京传播规律的研究
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摘要
传染性非典型肺炎,又称严重急性呼吸综合症传染(Severe AcuteRespiratory Syndrome,SARS),是由SARS冠状病毒感染引起的新发急性传染病.2002年11月在我国广东省首次发现后,至2003年6月,在短短时间里,蔓延肆虐于世界32个国家和地区,患者达八千多例,死亡七百多人,其中中国内地5327例(其中广东报告1512例),死亡349例(其中广东报告58例).2004年广东又发现4个新发病例,此外,台湾、新加坡、和我国还发生过实验室感染事故,SARS已成为二十一世纪首个对人类健康造成严重危害的传染病.
研究SARS的传播规律,一方面可以使我们从理论上了解SARS的传播规律;另一方面,为将来出现其它感染性疾病提供预防和治疗措施.
本文首先回顾了前人对SARS的研究现状,他们是采用Malthus模型和Logistic模型对SARS在北京的传播情况进行拟合的,也有采用SIR模型对北京SARS疫情的流行规律进行拟合的,拟合效果较好,但是这些模型都过于理想化;于是,有必要进行进一步研究,在这里用随机网络理论来探讨SARS在北京的传播,同时得到了相应结论,并提出了合理的预防措施.
通过比较,可以看出,虽然前人的研究可以使我们很直观的了解SARS病例随时间变化的情况,但是它只是一种事后描述;使用随机网络理论可以得到当传染能力T<0.0375时,疾病不会大规模流行.
Severe acuteres respiratory syndorme (SARS) caused by SARS coron-avirus (SARS-CoV) inefcted, found firstly in Gunagdong in Nov. 2002, is a new acute infectious disease. The outbreak of SARS during the spring of 2003 spread quickly to 32 countries or areas all over the world. There were more than 8000 reported SARS cases, more than 700 death cases. In China, There were 5327 reported SARS cases(1512 cases in Guangdong), 349 death cases (58 cases in Gunagdong). spring of 2004, there were 4 newly SARS cases in Gunagdong, besides, several SARS inefcting accidents happened at lab in Taiwan, Sigpaoer, China. SARS has become a new infectious disease which seriously threatens human health.
To investigate the transmission rule of SARS, In one place, we can get the transmission rule in theory; In the other place, it can provide evidence for prevention and control to other infectious diseases.
In the text, first of all, we review the study provided by others, such as taking advantage of the Malthus model and the Logistic model to fit the transmission rule of SARS, in Beijing. The other resort to the SIR model to fit the transmission rule of SARS, in Beijing. they're well, but they're too ideal; So, we should do some deeper study, in this paper, we investigate the transmission of SARS in Beijing with Random network theory, and provide well result and feasible methods about prevention.
After Comparing, we can see that, Although the past model can made us learn the rule directly, but it's only a discription after SARS outbreak. we also can get that, When T is smaller than 0.0375, SARS can't reach big outbreak, by Random network theory.
研究SARS的传播规律,一方面可以使我们从理论上了解SARS的传播规律;另一方面,为将来出现其它感染性疾病提供预防和治疗措施.
本文首先回顾了前人对SARS的研究现状,他们是采用Malthus模型和Logistic模型对SARS在北京的传播情况进行拟合的,也有采用SIR模型对北京SARS疫情的流行规律进行拟合的,拟合效果较好,但是这些模型都过于理想化;于是,有必要进行进一步研究,在这里用随机网络理论来探讨SARS在北京的传播,同时得到了相应结论,并提出了合理的预防措施.
通过比较,可以看出,虽然前人的研究可以使我们很直观的了解SARS病例随时间变化的情况,但是它只是一种事后描述;使用随机网络理论可以得到当传染能力T<0.0375时,疾病不会大规模流行.
Severe acuteres respiratory syndorme (SARS) caused by SARS coron-avirus (SARS-CoV) inefcted, found firstly in Gunagdong in Nov. 2002, is a new acute infectious disease. The outbreak of SARS during the spring of 2003 spread quickly to 32 countries or areas all over the world. There were more than 8000 reported SARS cases, more than 700 death cases. In China, There were 5327 reported SARS cases(1512 cases in Guangdong), 349 death cases (58 cases in Gunagdong). spring of 2004, there were 4 newly SARS cases in Gunagdong, besides, several SARS inefcting accidents happened at lab in Taiwan, Sigpaoer, China. SARS has become a new infectious disease which seriously threatens human health.
To investigate the transmission rule of SARS, In one place, we can get the transmission rule in theory; In the other place, it can provide evidence for prevention and control to other infectious diseases.
In the text, first of all, we review the study provided by others, such as taking advantage of the Malthus model and the Logistic model to fit the transmission rule of SARS, in Beijing. The other resort to the SIR model to fit the transmission rule of SARS, in Beijing. they're well, but they're too ideal; So, we should do some deeper study, in this paper, we investigate the transmission of SARS in Beijing with Random network theory, and provide well result and feasible methods about prevention.
After Comparing, we can see that, Although the past model can made us learn the rule directly, but it's only a discription after SARS outbreak. we also can get that, When T is smaller than 0.0375, SARS can't reach big outbreak, by Random network theory.
引文
[1]黄德生,关鹏,周宝森.SIR模型对北京市SARS疫情流行规律的拟合研究.R563.1;R181.25.2004年.
[2]王新为,李劲松,金敏.SARS冠状病毒的抵抗力研究.环境与健康杂志2004年3月第21卷第2期.2004年.
[3]Simon AL,Tornas GH.Applied rnathernatical ecology[M].Berlin:springer,119-145.1989.
[4]Becker NG,Britton T.Statistical studies of infectious disease incidence[J].Journal of Royal Statistical Society,Series B61(2):287-307.1999.
[5]Fouchier R,Kuiken T.Sehutten M,etal.Koch's Postulates fulfilled for SARS viurs.
[6]张传海,王一飞.SARS及其病原体研究进展.生命科学.Vol.15,No.3.2003年.
[7]黄吉城.SARS的实验室诊断和基因芯片在SARS检测中的应用.http://ckrd.cnki.net.
[8]M.Lipsitch et al.Transmission Dynamics and Control of Severe Acute Respiratory Syndrome.Science.2003.
[9]G.Chowell et al.Journal of Theoretical Biology 224,1-8.2003.
[10]《人口增长模型》.http://202.115.21.138/wlxt/ncourse/mathlab/web/jpl/zhanl/4.pdf.
[11]M.E.J.Newman.Spread of epidemic disease on networks.PHYSICAL REVIEW E 66,016128.2002.
[12]邦迪,U.S.A默蒂.图论及其应用.科学出版社.1987年.
[13]兰家隆,刘军.应用图论与算法.电子科技大学出版社.1995年.
[14]肖位枢.图论及其算法.航空工业出版社.1993年.
[15]杨炳儒.图论概要.天津科学技术出版社.1985年.
[16]陈树柏.网络图论及其应用.科学出版社.1963年.
[17]邱关源.网络图论简介.人民教育出版社.1978年.
[18]张忠志.复杂网络的演化模型研究.大连理工大学出版社.2006年.
[19]2003竞赛试题CUMCM-2003 Contest Problems.www.mcm.edu.cn.
[20]盛沛东.流行病蔓延时的一类方程[J].数理医药学杂志8(4);297-299.1995年.
[21]M.E.J.Newman.Are randomly grown graphs really random?.PHYSICAL REVIEW E,VOLUME 64,041902,2000.
[22]Lauren Ancel Meyers.Network theory and SARS:predicting outbreak diversity.Science Journal of Theoretical Biology 232(2005)71-81,2004.
[2]王新为,李劲松,金敏.SARS冠状病毒的抵抗力研究.环境与健康杂志2004年3月第21卷第2期.2004年.
[3]Simon AL,Tornas GH.Applied rnathernatical ecology[M].Berlin:springer,119-145.1989.
[4]Becker NG,Britton T.Statistical studies of infectious disease incidence[J].Journal of Royal Statistical Society,Series B61(2):287-307.1999.
[5]Fouchier R,Kuiken T.Sehutten M,etal.Koch's Postulates fulfilled for SARS viurs.
[6]张传海,王一飞.SARS及其病原体研究进展.生命科学.Vol.15,No.3.2003年.
[7]黄吉城.SARS的实验室诊断和基因芯片在SARS检测中的应用.http://ckrd.cnki.net.
[8]M.Lipsitch et al.Transmission Dynamics and Control of Severe Acute Respiratory Syndrome.Science.2003.
[9]G.Chowell et al.Journal of Theoretical Biology 224,1-8.2003.
[10]《人口增长模型》.http://202.115.21.138/wlxt/ncourse/mathlab/web/jpl/zhanl/4.pdf.
[11]M.E.J.Newman.Spread of epidemic disease on networks.PHYSICAL REVIEW E 66,016128.2002.
[12]邦迪,U.S.A默蒂.图论及其应用.科学出版社.1987年.
[13]兰家隆,刘军.应用图论与算法.电子科技大学出版社.1995年.
[14]肖位枢.图论及其算法.航空工业出版社.1993年.
[15]杨炳儒.图论概要.天津科学技术出版社.1985年.
[16]陈树柏.网络图论及其应用.科学出版社.1963年.
[17]邱关源.网络图论简介.人民教育出版社.1978年.
[18]张忠志.复杂网络的演化模型研究.大连理工大学出版社.2006年.
[19]2003竞赛试题CUMCM-2003 Contest Problems.www.mcm.edu.cn.
[20]盛沛东.流行病蔓延时的一类方程[J].数理医药学杂志8(4);297-299.1995年.
[21]M.E.J.Newman.Are randomly grown graphs really random?.PHYSICAL REVIEW E,VOLUME 64,041902,2000.
[22]Lauren Ancel Meyers.Network theory and SARS:predicting outbreak diversity.Science Journal of Theoretical Biology 232(2005)71-81,2004.