关于给定度数随机图上马尔可夫 SIR 流行病的说明

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2024-03-24 DOI:10.1007/s10959-024-01320-w

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引用次数: 0

摘要

摘要我们考虑了在接触图上传播 SIR 流行病的马尔可夫模型，该接触图是从具有 n 个顶点和给定顶点度的所有图集中均匀随机抽取的。Janson、Luczak 和 Windridge（Random Struct Alg 45(4):724-761, 2014）证明，这种流行病的演化可以通过一组简单微分方程的解很好地近似，从而为 Miller（J Math Biol 62(3):349-358, 2011）和 Volz（J Math Biol 56(3):293-310, 2008）的研究提供了概率论基础。本文对 Janson、Luczak 和 Windridge (Random Struct Alg 45(4):724-761, 2014) 中的极限确定性函数提供了额外的概率解释，从而进一步阐明了他们的结果与 Miller 和 Volz 的结果之间的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees

Abstract

We consider a Markovian model of an SIR epidemic spreading on a contact graph that is drawn uniformly at random from the set of all graphs with n vertices and given vertex degrees. Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014) prove that the evolution of such an epidemic is well approximated by the solution to a simple set of differential equations, thus providing probabilistic underpinnings to the works of Miller (J Math Biol 62(3):349–358, 2011) and Volz (J Math Biol 56(3):293–310, 2008). The present paper provides an additional probabilistic interpretation of the limiting deterministic functions in Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014), thus clarifying further the connection between their results and the results of Miller and Volz.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.