基于改进MCMC的疫情人群管控模型
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Epidemic Population Control Model Based on Improved MCMC
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    摘要:

    基于改进的马尔可夫链蒙特卡罗方法,探寻人群管制方式下疫情的传播与演化规律。首先在经典SEIR模型的基础上,建立SEDIQR模型,使用马尔可夫链蒙特卡罗方法估计出模型的参数,通过Geweke方法对马氏链进行收敛诊断,并用基本再生矩阵理论推导出疫情的有效再生数表达式。然后用韩国的疫情数据进行实证分析,并进行管控力度分析。结果表明:模型得到的理论值与实际值吻合较好,有效再生数的变化趋势能够合理地反映疫情传播能力的变化;减小初始易感者数量和有效接触率均能够降低现有确诊人数和感染者人数的峰值和峰值时间,且能够缩短有效再生数降为1所需的时间,初始易感者数量和有效接触率都是影响疫情发展的重要敏感参数,同幅度地控制初始易感者的数量,相对于控制有效接触率,对于防控疫情具有更大的作用。新的人群管制方式下的疫情传播模型预测的结果比之前文献预测的要更准确一些。疫情的传播与演化规律对政府管理部门和相关医疗专家制定和修正防疫方案具有重要的参考价值,并且可为世界各国防御类似疫情提供理论依据。

    Abstract:

    The intrinsic law of epidemic spread and evolution under crowd control mode is explored based on the improved Markov chain Monte Carlo method (Metropolis–Hastings method). First of all,?based on the classical SEIR?model, ?the?SEDIQR model is established, and the model?parameters?by?Markov?chain Monte Carlo method is established. At?the?same time, the convergence of Markov chain is diagnosed by Geweke method,?and?the?expression of effective regeneration number of epidemic situation?was deduced?by?using?basic regeneration matrix theory. Then, the epidemic data of South Korea is used for empirical analysis and?further analyzed?the?strength?of management and?control. The results show that the theoretical value obtained by the model is in good agreement with the actual value, and the?changing?trend of effective regeneration number can reasonably reflect the change of epidemic spreading ability.Besides,reducing the?number of initial?susceptible?population?and effective contact rate can reduce the peak value and peak time of the number of confirmed?patients?and infected?patients,?and shorten the time?needed to reduce?the?number of?effective regeneration?to one. And the number of initial susceptible?population?and effective contact rate are important sensitive parameters?affecting?the development of?epidemic, controlling the number of initially susceptible persons at the same range has a greater effect on the prevention and control of the epidemic than controlling the effective exposure rate. Under?the new crowd control?model, the prediction results of epidemic spread model?are more accurate than those predicted by previous?literature.Meanwhile,the?intrinsic?law of epidemic spread and evolution?has?important reference value for the administrative departments of government and?related?medical experts to formulate and revise epidemic prevention programs, and for the world in the prevention of similar epidemic provides a theoretical basis.

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郑辰彦,王露露,胡益传.基于改进MCMC的疫情人群管控模型[J].科技与产业,2022,22(03):352-362

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  • 在线发布日期: 2022-03-28