School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Math Biosci. 2010 Apr;224(2):53-73. doi: 10.1016/j.mbs.2009.12.003. Epub 2009 Dec 22.
This paper is concerned with a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.
本文研究了一类带有随机网络社交接触且具有家庭隔离的传染病传播的随机 SIR（易感染者-感染者-移除者）模型。研究了在适当的方式下，当人口规模趋于无穷大时模型的行为。获得了一个阈值参数，该参数决定了初始感染者数量较少的传染病是否能够建立并导致大规模爆发，并获得了大规模爆发发生的概率和最终被这种爆发感染的人口比例的预期值，以及计算这些数量的方法。蒙特卡罗模拟表明，即使对于中等规模的有限群体，这些渐近数量也能准确反映有限群体的行为。将该模型与文献中以前研究过的相关模型进行了比较和对比。还探讨了总体人群结构中的聚类程度和传染性期分布对模型结果的影响。
