Repository logo
 
Publication

Dynamics of Epidemiological Models

2010-07-27Journal article Open access
Simple item page
datacite.subject.fosHumanidades::Filosofia, Ética e Religião
datacite.subject.fosCiências Naturais::Matemáticas
datacite.subject.fosCiências Agrárias::Agricultura, Silvicultura e Pescas
dc.contributor.authorPinto, Alberto
dc.contributor.authorAguiar, Maíra
dc.contributor.authorMartins, José
dc.contributor.authorStollenwerk, Nico
dc.date.accessioned2025-11-05T17:51:22Z
dc.date.available2025-11-05T17:51:22Z
dc.date.issued2010-07-27
dc.description.abstractWe study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation.eng
dc.description.sponsorshipWe thank LIAAD-INESC Porto LA, Calouste Gulbenkian Foundation, PRODYNESF, POCTI and POSI by FCT and Ministério da Ciência e da Tecnologia, and the FCT Pluriannual Funding Program of the LIAAD-INESC Porto LA and of the Research Center of Mathematics of University of Minho, for their financial support. J. Martins also acknowledge the financial support from the FCT grant with reference SFRW/BD/37433/2007. Part of this research was developed during a visit by the authors to the CUNY, IHES, IMPA, MSRI, SUNY, Isaac Newton Institute, University of Berkeley and University of Warwick. We thank them for their hospitality.
dc.identifier.citationPinto, A., Aguiar, M., Martins, J. et al. Dynamics of Epidemiological Models. Acta Biotheor 58, 381–389 (2010). https://doi.org/10.1007/s10441-010-9116-7.
dc.identifier.doi10.1007/s10441-010-9116-7
dc.identifier.eissn1572-8358
dc.identifier.issn0001-5342
dc.identifier.urihttp://hdl.handle.net/10400.8/14532
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relation.hasversionhttps://link.springer.com/article/10.1007/s10441-010-9116-7
dc.relation.ispartofActa Biotheoretica
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectEpidemic models
dc.subjectQuasi-stationary states
dc.subjectPair approximation
dc.titleDynamics of Epidemiological Modelseng
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage389
oaire.citation.startPage381
oaire.citation.titleActa Biotheoretica
oaire.citation.volume58
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

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Dynamics of Epidemiological Models.pdf
Size:
97.92 KB
Format:
Adobe Portable Document Format
Description:
We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation.
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.32 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

ESTG - Artigos em revistas internacionais