Stationarity in moment closure and quasi-stationarity of the SIS model

Martins, José; Alberto Pinto; Nico Stollenwerk

Publication

Stationarity in moment closure and quasi-stationarity of the SIS model

2012-04Journal article

datacite.subject.fos	Ciências Naturais::Ciências Biológicas
datacite.subject.fos	Ciências Naturais::Matemáticas
datacite.subject.sdg	03:Saúde de Qualidade
datacite.subject.sdg	07:Energias Renováveis e Acessíveis
datacite.subject.sdg	11:Cidades e Comunidades Sustentáveis
dc.contributor.author	Martins, José
dc.contributor.author	Alberto Pinto
dc.contributor.author	Nico Stollenwerk
dc.date.accessioned	2026-01-09T16:33:52Z
dc.date.available	2026-01-09T16:33:52Z
dc.date.issued	2012-04
dc.description.abstract	Previous epidemiological studies on SIS model have only considered the dynamic evolution of the mean value and the variance of the infected individuals. In this paper, through cumulant neglection, we use the dynamic equations of all the moments of infected individuals to develop a recursive method to compute the equilibria manifold of the moment closure ODE’s. Specifically, we use the stable equilibria of the moment closure ODE’s to obtain good approximations of the quasi-stationary states of the SIS model. This is a crucial step when the quasi-stationary distribution is highly skewed.	eng
dc.description.sponsorship	The authors are grateful to the anonymous referees for their valuable comments and suggestions. We thank LIAAD-INESC Porto LA, Calouste Gulbenkian Foundation, Programs FEDER, POCTI and POCI by FCT and Ministério da Ciência, Tecnologia e Ensino Superior and Centro de Matemática da Universidade do Minho and Centro de Matemática e Aplicações Fundamentais da Universidade de Lisboa for their financial support. José Martins also acknowledge the financial support from the FCT Grant with reference SFRW/BD/37433/2007. This work has been further supported by the European Union under FP7 in the EPIWORK project and the Portuguese FCT project PTDC/MAT/115168/2009.
dc.identifier.citation	José Martins, Alberto Pinto, Nico Stollenwerk, Stationarity in moment closure and quasi-stationarity of the SIS model, Mathematical Biosciences, Volume 236, Issue 2, 2012, Pages 126-131, ISSN 0025-5564, https://doi.org/10.1016/j.mbs.2012.02.001.
dc.identifier.doi	10.1016/j.mbs.2012.02.001
dc.identifier.issn	0025-5564
dc.identifier.uri	http://hdl.handle.net/10400.8/15277
dc.language.iso	eng
dc.peerreviewed	yes
dc.publisher	Elsevier
dc.relation.hasversion	https://www.sciencedirect.com/science/article/pii/S002555641200017X?via%3Dihub
dc.relation.ispartof	Mathematical Biosciences
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject	SIS model
dc.subject	Moment closure
dc.subject	Quasi-stationary states
dc.title	Stationarity in moment closure and quasi-stationarity of the SIS model	eng
dc.type	journal article
dspace.entity.type	Publication
oaire.citation.endPage	131
oaire.citation.issue	2
oaire.citation.startPage	126
oaire.citation.title	Mathematical Biosciences
oaire.citation.volume	236
oaire.version	http://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyName	Gouveia Martins
person.givenName	José Maria
person.identifier.ciencia-id	9015-9D8C-93DF
person.identifier.gsid	43461781600
person.identifier.orcid	0000-0002-0556-7861
relation.isAuthorOfPublication	29fc5be8-b5a2-489c-92d3-c0efe7e57892
relation.isAuthorOfPublication.latestForDiscovery	29fc5be8-b5a2-489c-92d3-c0efe7e57892