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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

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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

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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
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