AN SIR EPIDEMIC MODEL ON A POPULATION WITH RANDOM NETWORK AND HOUSEHOLD STRUCTURE, AND SEVERAL TYPES OF INDIVIDUALS
AN SIR EPIDEMIC MODEL ON A POPULATION WITH RANDOM NETWORK AND HOUSEHOLD STRUCTURE, AND SEVERAL TYPES OF INDIVIDUALS
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DOI：
10.1239/aap/1331216645
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发表时间：
2012-03-01
影响因子：
1.2
通讯作者：
Sirl, David
中科院分区：
文献类型：
--
作者：
Ball, Frank;Sirl, David
我们考虑了一类具有多种类型个体的随机SIR(易感-感染-移除)传染病模型。有传染性的人可以在两个层面上进行传染性接触，在他们自己的“家庭”内，以及在代表额外社会接触的随机图表中与他们的邻居进行接触。该随机图是众所周知的配置模型的扩展，以允许几种类型的个体。给出了强逼近定理，得到了流行病模型的阈值定理，并给出了在初始感染人数较少的情况下计算大爆发概率的方法。Ball，Sirl和TRapman(2009)的一个定理的多类型类比启发了一种计算如此大的疫情预期规模的方法。我们还考虑了疫苗接种，并给出了我们结果的一些简短的数字说明。
We consider a stochastic SIR (susceptible -> infective -> removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own 'household' and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball, Sirl and Trapman (2009) heuristically motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results.