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A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

2010-11Journal article Open access
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datacite.subject.fosCiências Agrárias::Outras Ciências Agrárias
dc.contributor.authorStollenwerk, Nico
dc.contributor.authorvan Noort, Sander
dc.contributor.authorMartins, José
dc.contributor.authorAguiar, Maíra
dc.contributor.authorHilker, Frank
dc.contributor.authorPinto, Alberto
dc.contributor.authorGomes, Gabriela
dc.date.accessioned2025-11-06T15:23:18Z
dc.date.available2025-11-06T15:23:18Z
dc.date.issued2010-11
dc.descriptionFonte: https://www.tandfonline.com/doi/10.1080/17513758.2010.487159?url_ver=Z39.88-2003&rfr_id=ori:rid:crossref.org&rfr_dat=cr_pub%20%200pubmed
dc.description.abstractRecently, 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.eng
dc.description.sponsorshipNico Stollenwerk thanks Peter Grassberger, Jülich, for pointing his attention to the partial immunization models investigated in the physics literature and further discussions on these models. Further thanks to Friedhelm Drepper, Jülich, Vincent Jansen, London, and Minus van Baalen, Paris, on various aspects of the present manuscript. José Martins and Maíra Aguiar also acknowledge the financial support from the FCT grants with references SFRW/BD/37433/2007, respectively, SFRH/BD/43236/2008. Thiswork has been further supported by the European Union under FP7 in the EPIWORKproject.
dc.identifier.citationStollenwerk, N., van Noort, S., Martins, J., Aguiar, M., Hilker, F., Pinto, A., & Gomes, G. (2010). A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold. Journal of Biological Dynamics, 4(6), 634–649. https://doi.org/10.1080/17513758.2010.487159.
dc.identifier.doi10.1080/17513758.2010.487159
dc.identifier.eissn1751-3766
dc.identifier.issn1751-3758
dc.identifier.urihttp://hdl.handle.net/10400.8/14543
dc.language.isoeng
dc.peerreviewedyes
dc.publisherTaylor and Francis
dc.relation.hasversionhttps://www.tandfonline.com/doi/full/10.1080/17513758.2010.487159
dc.relation.ispartofJournal of Biological Dynamics
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectSIRI model
dc.subjectcritical threshold
dc.subjectcompact growth
dc.subjectannular growth
dc.titleA spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection thresholdeng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage649
oaire.citation.issue6
oaire.citation.startPage634
oaire.citation.titleJournal of Biological Dynamics
oaire.citation.volume4
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameGouveia Martins
person.givenNameJosé Maria
person.identifier.orcid0000-0002-0556-7861
relation.isAuthorOfPublication29fc5be8-b5a2-489c-92d3-c0efe7e57892
relation.isAuthorOfPublication.latestForDiscovery29fc5be8-b5a2-489c-92d3-c0efe7e57892

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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.
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