{"title":"A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees","authors":"","doi":"10.1007/s10959-024-01320-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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 <em>n</em> 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.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"14 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Theoretical Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01320-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.
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