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

Pub Date : 2024-03-24 DOI:10.1007/s10959-024-01320-w

引用次数: 0

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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关于给定度数随机图上马尔可夫 SIR 流行病的说明

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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