具有随机易感性水平的里德-弗罗斯特流行病模型的维度
The dimension of Reed-Frost epidemic models with randomized susceptibility levels.
作者信息
Picard P, Lefèvre C
机构信息
Mathématiques Appliquées, Université de Lyon I, Villeurbanne, France.
出版信息
Math Biosci. 1991 Dec;107(2):225-33. doi: 10.1016/0025-5564(91)90006-5.
A generalized Reed-Frost epidemic process is discussed in which variability among susceptible individuals is incorporated by randomizing the levels of resistance of the individuals to the infection. Our purpose is to derive the exact distribution of the ultimate number of susceptibles surviving the disease. This is achieved by a simple conditional argument and by using a particular family of polynomials defined recursively. The results can be viewed as a continuation of those obtained by the authors for the alternative situation with randomized infectivity levels.
讨论了一种广义的里德 - 弗罗斯特流行病过程，其中通过随机确定个体对感染的抵抗力水平来纳入易感个体之间的变异性。我们的目的是推导出疾病流行后幸存易感者最终数量的精确分布。这通过一个简单的条件论证以及使用一个递归定义的特定多项式族来实现。这些结果可以看作是作者在随机感染水平的替代情况下所获得结果的延续。
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