Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/98758
Author(s): N. Stollenwerk
S. van Noort
J. Martins
M. Aguiar
F. Hilker
A. A. Pinto
G. Gomes
Title: A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold
Issue Date: 2010
Abstract: 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.
Description: 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.
Subject: Matemática
Mathematics
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
URI: https://hdl.handle.net/10216/98758
Document Type: Artigo em Revista Científica Internacional
Rights: restrictedAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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