时滞离散SEIR模型在评价水痘暴发疫情防控措施效果中的应用

郑庆鸣; 王铁强

doi:10.3784/j.issn.1003-9961.2017.10/11.023

时滞离散SEIR模型在评价水痘暴发疫情防控措施效果中的应用

Application of a discrete time delay SEIR model in evaluation of varicella control measures

摘要

摘要: 目的运用时滞离散SEIR模型预测水痘暴发疫情发病数，以评估疫情控制措施的实际应用效果。方法采用时滞离散SEIR模型对暴发疫情数据进行模拟，评价病例隔离、应急接种等疫情控制措施的实施效果。结果不采取任何干预措施时，模拟水痘暴发疫情理论的发病数为434人，罹患率为30.58%（434/1 419），流行过程历时3个月，发病高峰在首发病例发生后60天，流行过程中可见明显的代际现象，每代间隔2周左右。模拟在首发病例发病当日、第14、28、42天开始实施100%病例隔离，总发病数分别为5、13、34和78人。模拟在首发病例发病后第14天采取病例隔离措施，隔离率分别为30%、50%、70%和90%时，总发病数分别为370、323、230和52人。模拟首发病例发病当日、第14、28和42天时实施应急接种，接种率100%时，总发病数分别为5、14、37和84人。模拟首发病例发病后第14天实施应急接种，接种率分别为30%、50%、70%和90%时，总发病数分别为262、150、52和19人。本文模拟的水痘暴发疫情实际发病118人，隔离率为82.20%（97/118），模拟首发病例发病后第30天采取病例隔离措施，隔离率82.20%，理论总发病数为148人，比实际发病多30人。结论时滞离散SEIR模型能较好地预测水痘暴发疫情规模，可从理论上评价防控措施对疫情的影响；尽早严格实施病例隔离和高覆盖率的应急接种均是有效的水痘疫情控制措施。

Abstract: Objective To predict the epidemic trend and evaluate the theoretical effect of the case isolation and emergent vaccination in a varicella outbreak control with a discrete time delay SEIR model. Methods The model was discretized on a SEIR continuous model. The time delay effects of latent period and infectious period were took into account as well. The theoretical number of cases could be obtained and theoretical effect of the control measures could be evaluated by the model. Results Without any control measures, the theoretical attack rate was 30.58% (434/1 419). The outbreak lasted 3 months and the peak epidemic time was 60 days after the onset of the first case. Generation phenomenon was observed with the interval of two weeks. With the isolation of all cases on day 0, 14, 28 and 42 after the onset of the first case, the theoretical number of cases were 5, 13, 34 and 78, respectively. With case isolation on day 14 after the onset of the first case and the case isolation rates of 30%, 50%, 70% and 90%, the theoretical number of cases were 370, 323, 230 and 52, respectively. With the emergent vaccination for all persons on day 0, 14, 28, 42 after the onset of the first case, the theoretical number of cases were 5, 14, 37 and 84, respectively. With the emergent vaccination on 14 days after the onset of the first case and the coverage rates of 30%, 50%, 70% and 90%, the theoretical number of cases were 262, 150, 52 and 19, respectively. The actual cases number of the varicella outbreak was 118, and the actual case isolation rate was 82.20%. With the case isolation on day 30 after the onset of the first case and the case isolation rate of 82.20%, the theoretical number of cases was 148, 30 cases more than actual case number. Conclusion The discrete time delay SEIR model can be used to predict varicella epidemic trend, and evaluate the theoretical effect of the control measures in varicella outbreak. Both case isolation and emergent vaccination with high coverage rate in the early stage of a varicella outbreak are effective for ending the outbreak.

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