{"title":"费勒过程驱动的SIR流行病","authors":"Matthieu Simon","doi":"10.1017/jpr.2023.2","DOIUrl":null,"url":null,"abstract":"\n We consider a stochastic SIR (susceptible \n \n \n \n$\\rightarrow$\n\n \n infective \n \n \n \n$\\rightarrow$\n\n \n removed) model in which the infectious periods are modulated by a collection of independent and identically distributed Feller processes. Each infected individual is associated with one of these processes, the trajectories of which determine the duration of his infectious period, his contamination rate, and his type of removal (e.g. death or immunization). We use a martingale approach to derive the distribution of the final epidemic size and severity for this model and provide some general examples. Next, we focus on a single infected individual facing a given number of susceptibles, and we determine the distribution of his outcome (number of contaminations, severity, type of removal). Using a discrete-time formulation of the model, we show that this distribution also provides us with an alternative, more stable method to compute the final epidemic outcome distribution.","PeriodicalId":50256,"journal":{"name":"Journal of Applied Probability","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SIR epidemics driven by Feller processes\",\"authors\":\"Matthieu Simon\",\"doi\":\"10.1017/jpr.2023.2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n We consider a stochastic SIR (susceptible \\n \\n \\n \\n$\\\\rightarrow$\\n\\n \\n infective \\n \\n \\n \\n$\\\\rightarrow$\\n\\n \\n removed) model in which the infectious periods are modulated by a collection of independent and identically distributed Feller processes. Each infected individual is associated with one of these processes, the trajectories of which determine the duration of his infectious period, his contamination rate, and his type of removal (e.g. death or immunization). We use a martingale approach to derive the distribution of the final epidemic size and severity for this model and provide some general examples. Next, we focus on a single infected individual facing a given number of susceptibles, and we determine the distribution of his outcome (number of contaminations, severity, type of removal). Using a discrete-time formulation of the model, we show that this distribution also provides us with an alternative, more stable method to compute the final epidemic outcome distribution.\",\"PeriodicalId\":50256,\"journal\":{\"name\":\"Journal of Applied Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-05-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Probability\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/jpr.2023.2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/jpr.2023.2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
We consider a stochastic SIR (susceptible
$\rightarrow$
infective
$\rightarrow$
removed) model in which the infectious periods are modulated by a collection of independent and identically distributed Feller processes. Each infected individual is associated with one of these processes, the trajectories of which determine the duration of his infectious period, his contamination rate, and his type of removal (e.g. death or immunization). We use a martingale approach to derive the distribution of the final epidemic size and severity for this model and provide some general examples. Next, we focus on a single infected individual facing a given number of susceptibles, and we determine the distribution of his outcome (number of contaminations, severity, type of removal). Using a discrete-time formulation of the model, we show that this distribution also provides us with an alternative, more stable method to compute the final epidemic outcome distribution.
期刊介绍:
Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used.
A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.