您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（医学版）》

山东大学学报（医学版） ›› 2016, Vol. 54 ›› Issue (9): 87-91.doi: 10.6040/j.issn.1671-7554.0.2016.042

• • 上一篇    下一篇

SIR模型在成人麻疹爆发及其疫情控制评价中的应用

罗成1,许青2,孙霖3,章涛1,李润滋1,刘言训1,薛付忠1,李秀君1   

  1. 1.山东大学公共卫生学院生物统计系, 山东 济南 250012;2.山东省疾病预防控制中心免疫预防管理所, 山东 济南 250014;3.山东大学金融研究院, 山东 济南 250100
  • 收稿日期:2016-01-12 出版日期:2016-09-10 发布日期:2016-09-10
  • 通讯作者: 李秀君. E-mail:xjli@sdu.edu.cn E-mail:xjli@sdu.edu.cn
  • 基金资助:
    山东省科技发展计划(2014GGH218019);病原微生物生物安全国家重点实验室开放课题(SKLPBS1453);山东省泰山学者岗位支持

Use of SIR model in evaluation of control measures for adults measles outbreak

LUO Cheng1, XU Qing2, SUN Lin3, ZHANG Tao1, LI Runzi1, LIU Yanxun1, XUE Fuzhong1, LI Xiujun1   

  1. 1. Department of Biostatics, School of Public Health, Shandong University, Jinan 250012, Shandong, China;
    2. Shandong Center for Disease Control and Prevention, Institute of Immunization Manage, Jinan 250014, Shandong, China;
    3. Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China
  • Received:2016-01-12 Online:2016-09-10 Published:2016-09-10

PDF (PC)

587

摘要： 目的 利用SIR模型,探讨成人麻疹爆发疫情的传播过程及疫苗控制效果。 方法 在一定的假设条件下,根据一定时期内实际爆发麻疹发病数,建立传染病动力学模型,利用马尔科夫蒙特卡洛算法对SIR模型进行参数估计。通过合理假设计算基本再生数(R0)和有效再生数(Rt),研究疫苗控制效果。结果〓本次麻疹爆发有效接触率β=0.001 06,恢复率γ=0.117, R0=2.96;在该模型假定条件下,如果在病例出现的第2天开始接种疫苗,可减少90.6%的病例发生,而在当前真实感染及控制措施下,该爆发在第26天时Rt<1,此时疾病即使不采取任何防治措施,亦会逐渐消失。 结论 SIR模型适用于研究成人麻疹爆发过程,其在参数估计及模型拟合中接近真实情况。

关键词: 传染病动力学模型, 麻疹, SIR模型, 基础再生数, 马尔科夫蒙特卡洛

Abstract: Objective A susceptible-infectious-recovered(SIR)model was established to describe the process of measles outbreak, and to analyze the control effect of vaccination and optimal control strategy. Methods Under the special circumstances, we adopted Markov Chain Monte Carlo(MCMC)to estimate the parameters of the model based on the real infected numbers. We calculated the basic reproduction number(R0)and effective reproduction number(Rt)base on rational assumptions to analyze the control effect of vaccination. Results The effective contact rate β was 0.001 06, the recovery rate γ was 0.117 and R0 was 2.96. The percentage of patients could reduce by 90.6% if emergency vaccination was used the second day after outbreak. On the 26th day, Rt<1, and the disease would fade away even if there were no vaccination. Conclusion The SIR model is suitable for studying adults’ measles outbreak, and it is close to real situation in estimating parameters.

Key words: Mathematical models of infectious diseases, Measles, SIR Model, Basic Reproduction Number, Markov Chain Monte Carlo

中图分类号: 

  • R183.9
[1] 马超, 中国麻疹流行病学与消除麻疹免疫策略研究[D]. 北京: 中国疾病预防控制中心, 2014.
[2] 马超, 苏琪茹, 郝利新, 等. 中国2012~2013年麻疹流行病学特征与消除麻疹进展[J]. 中国疫苗和免疫, 2014, 20(3): 193-199. MA Chao, SU Qiru, HAO Lixin, et al. Measles epidemiology characteristics and progress toward measles elimination in China[J]. Chinese Journal of Vaccines and Immunization, 2014, 20(3): 193-199.
[3] Grassly NC, Fraser C. Mathematical models of infectious disease transmission[J]. Nat Rev Micro, 2008, 6(6): 477-487.
[4] Sood N, Wagner Z, Jaycocks A, et al. Test-and-treat in Los Angeles: a mathematical model of the effects of test-and-treat for the population of men who have sex with men in Los Angeles County[J]. Clin Infect Dis, 2013, 56(12): 1789-1796.
[5] 马知恩,周义仓,王稳地,等. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2006.
[6] Chowell G, Blumberg S, Simonsen L, et al. Synthesizing data and models for the spread of MERS-CoV, 2013: key role of index cases and hospital transmission[J]. Epidemics, 2014, 9: 40-51, doi:10.1016/j.epidem.2014.09.011.
[7] 张秀敏. 一起成人麻疹爆发调查及其控制效果评价[D]. 济南: 山东大学, 2006.
[8] 许青, 徐爱强, 宋立志, 等. 一起成人麻疹爆发调查及其流行因素分析[J]. 中国计划免疫, 2007, 13(5): 440-443. XU Qing, XU Aiqiang, SONG Lizhi, et al. Epidemiological analysis on measles outbreak among adults[J]. Chinese Journal of Vaccines and Immunization, 2007, 13(5): 440-443.
[9] Roberts MG, Tobias MI. Predicting and preventing measles epidemics in New Zealand: application of a mathematical model[J]. Epidemiol Infect, 2000, 124(2): 279-287.
[10] Hamborsky J, Kriger K,Wolfe C. Epidemiology and prevention of vaccine-preventable diseases[M]. Washington: Centers for Disease Control and Prevention, 2015.
[11] 史建国,葛玉蕾. 麻疹疫苗应急接种控制爆发流行的效果[J]. 中华疾病控制杂志, 2002, 6(2): 147-148. SHI Jianguo, GE Yulei. Analysis of the control effect on outbreak and epidemic of measle with measle vaccine emergency vaccination[J]. Chinese Journal of Disease Control & Prevention, 2002, 6(2): 147-148.
[12] Haario H, Laine M, Mira A, et al. DRAM: Efficient adaptive MCMC[J]. Statist Comput, 2006, 16(4): 339-354.
[13] Haario H, Saksman E,Tamminen J. An adaptive Metropolis algorithm[J]. Bernoulli, 2001, 7(2): 223-242.
[14] Bonacic Marinovic AA, Swaan C, Wichmann O, et al. Effectiveness and timing of vaccination during School measles outbreak[J]. Emerg Infect Dis, 2012, 18(9): 1405-1413.
[15] Appanna T, Aundhakar U. Parameter estimation of SIR epidemic model using MCMC methods[J]. Global J Pure Appl Math, 2016, 12(2): 1299-1306.
[16] Morton A, Finkenstädt BF. Discrete time modelling of disease incidence time series by using Markov chain Monte Carlo methods[J]. J Roy Statist Soc Ser C, 2005, 54(3): 575-594.
[17] Pandey A. Modelling dengue transmission and vaccination[D]. Clemson: Clemson University, 2014.
[18] Durrheim D, Crowcroft N, Strebel P. Measles — The epidemiology of elimination[J]. Vaccine, 2014, 32(51): 6880-6883.
[19] Fred B, Pauline D, Jianhong W. Mathematical epidemiology[M]. Heidelberg: Springer-Verlag, 2008.
[1] 唐小敏,张丽,叶绪芳,任刚,左丽. 贵州省2013年麻疹病毒核蛋白基因特征分析[J]. 山东大学学报（医学版）, 2017, 55(3): 70-74.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(医学版)》编辑部　
地址:山东大学科技期刊社（济南市历城区山大南路27号山东大学中心校区明德楼B座721室） 电话: 0531-88366918 E-mail: xbyxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发