Fierro R
Instituto de Matemáticas, Universidad Católica de Valparaíso, Chile.
J Math Biol. 1996;34(8):843-56. doi: 10.1007/BF01834822.
This paper considers the simplest stochastic model for the spread of an epidemic in a closed, homogeneously mixing population. Approximate methods are presented for calculating the probability distribution of the epidemic size (i.e. number of infected individuals). In fact, a functional central limit theorem and a large deviation principle for the epidemic size when the population increases are shown. These results enable us to both obtain a global approximation for the epidemic size and study asymptotic properties of other random variables depending on the complete history of the epidemic. As an application of our results, we derive two sequences of estimators for the contact rate and analyze their asymptotic behaviour.
本文考虑了在封闭、均匀混合人群中传染病传播的最简单随机模型。提出了用于计算疫情规模（即感染个体数量）概率分布的近似方法。事实上，当人群规模增加时，给出了疫情规模的泛函中心极限定理和大偏差原理。这些结果使我们既能获得疫情规模的全局近似，又能研究依赖于疫情完整历史的其他随机变量的渐近性质。作为我们结果的一个应用，我们推导了接触率的两个估计量序列并分析了它们的渐近行为。
