文章基本信息

标题：A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold
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作者：Nico Stollenwerk ; Sander van Noort ; José Martins 等
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2010
卷号：4
期号：6
页码：634-649
DOI：10.1080/17513758.2010.487159
出版社：Taylor & Francis
摘要：Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.
关键词：SIRI model; critical threshold; compact growth; annular growth