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AN EPIDEMIC IN A DYNAMIC POPULATION WITH IMPORTATION OF INFECTIVES
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 3
2017 (English)In: The Annals of Applied Probability, ISSN 1050-5164, E-ISSN 2168-8737, Vol. 27, no 1, 242-274 p.Article in journal (Refereed) Published
Abstract [en]

Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size n. A Markovian SIR (susceptible -> infective -> recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where n -> infinity, keeping the basic reproduction number R-0 as well as the importation rate of infectives fixed, but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than 1/log n. It is shown that, as n -> infinity, the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible, infective and recovered, is encapsulated in a 1-dimensional regenerative process S = {S(t); t >= 0} describing the limiting fraction of the population that are susceptible. The process S grows deterministically, except at one random time point per regenerative cycle, where it jumps down by a size that is completely determined by the waiting time since the start of the regenerative cycle. Properties of the process S, including the jump size and stationary distributions, are determined.

Place, publisher, year, edition, pages
2017. Vol. 27, no 1, 242-274 p.
Keyword [en]
Branching process, regenerative process, SIR epidemic, Skorohod metric, weak convergence
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-142526DOI: 10.1214/16-AAP1203ISI: 000397363200009OAI: oai:DiVA.org:su-142526DiVA: diva2:1093954
Available from: 2017-05-08 Created: 2017-05-08 Last updated: 2017-05-08Bibliographically approved

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