Abstract

We present some stochastic model of an infection spread among the adult population of a certain region. The model bases on a random birth and death process supplemented by the point distributions that reflect the durations of stay of individuals at various stages of the disease. The durations of some stages of the disease are assumed constant. The model is a stochastic analog of a system of delay differential equations and convolution integral equations describing the infection spread in the deterministic approach. We address the problem of the infection eradication over a time span comparable to the average lifetime of several generations of individuals. The results of computational experiments are presented, where the dynamics of mathematical expectations of the size of certain groups of individuals is studied and the probability of the infection eradication over a finite time span is estimated using the Monte Carlo method.

中文翻译：

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基于非马尔可夫随机过程的阶段相关的流行病模型分析

摘要

我们提出了一种在特定区域的成年人口中传播的感染的随机模型。该模型基于随机的出生和死亡过程，并补充了点分布，该点分布反映了疾病各个阶段个体的停留时间。假定疾病某些阶段的持续时间是恒定的。该模型是延迟微分方程和卷积积分方程系统的随机模拟，描述了确定性方法中的感染扩散。我们解决了与几代人的平均寿命相当的一段时间内的根除感染的问题。给出了计算实验的结果，