Discrete and continuous SIS epidemic models: A unifying approach

Detalhes bibliográficos
Autor(a) principal: Chalub, Fábio Augusto da Costa Carvalho
Data de Publicação: 2014
Outros Autores: Souza, Max O.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/24759
Resumo: 550030/2010-7.
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spelling Discrete and continuous SIS epidemic models: A unifying approachDiffusive limitsDifferential equationsSIS epidemiological modelsIBM modellingDifferential equationsDiffusive limitsIBM modellingSIS epidemiological models550030/2010-7.The susceptible-infective-susceptible (SIS) epidemiological scheme is the simplest description of the dynamics of a disease that is contact-transmitted, and that does not lead to immunity. Two by now classical approaches to such a description are: (i) the use of a mass-action compartmental model that leads to a single ordinary differential equation (SIS-ODE); (ii) the use of a discrete-time Markov chain model (SIS-DTMC). While the former can be seen as a mean-field approximation of the latter under certain conditions, it is also known that their dynamics can be significantly different, if the basic reproduction number is greater than one. The goal of this work is to introduce a continuous model, based on a partial differential equation (SIS-PDE), that retains the finite populations effects present in the SIS-DTMC model, and that allows the use of analytical techniques for its study. In particular, it will reduce itself to the SIS-ODE model in many circumstances. This is accomplished by deriving a diffusion-drift approximation to the probability density of the SIS-DTMC model. Such a diffusion is degenerated at the origin, and must conserve probability. These two features then lead to an interesting consequence: the biologically correct solution is a measure solution. We then provide a convenient representation of such a measure solution that allows the use of classical techniques for its computation, and that also provides a tool for obtaining information about several dynamical features of the model. In particular, we show that the SIS-ODE gives the most likely state, conditional on non-absorption. As a further application of such representation, we show how to define the disease-outbreak probability in terms of the SIS-PDE model, and show that this definition can be used both for certain and uncertain initial presence of infected individuals. As a final application, we compute an approximation for the extinction time of the disease. In addition, we present many numerical examples that confirm the good approximation of the SIS-DTMC by the SIS-PDE.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNChalub, Fábio Augusto da Costa CarvalhoSouza, Max O.2017-10-30T23:00:54Z2014-062014-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/24759eng1476-945XPURE: 379760https://doi.org/10.1016/j.ecocom.2014.01.006info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T04:12:55Zoai:run.unl.pt:10362/24759Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:28:07.311912Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Discrete and continuous SIS epidemic models: A unifying approach
title Discrete and continuous SIS epidemic models: A unifying approach
spellingShingle Discrete and continuous SIS epidemic models: A unifying approach
Chalub, Fábio Augusto da Costa Carvalho
Diffusive limits
Differential equations
SIS epidemiological models
IBM modelling
Differential equations
Diffusive limits
IBM modelling
SIS epidemiological models
title_short Discrete and continuous SIS epidemic models: A unifying approach
title_full Discrete and continuous SIS epidemic models: A unifying approach
title_fullStr Discrete and continuous SIS epidemic models: A unifying approach
title_full_unstemmed Discrete and continuous SIS epidemic models: A unifying approach
title_sort Discrete and continuous SIS epidemic models: A unifying approach
author Chalub, Fábio Augusto da Costa Carvalho
author_facet Chalub, Fábio Augusto da Costa Carvalho
Souza, Max O.
author_role author
author2 Souza, Max O.
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Chalub, Fábio Augusto da Costa Carvalho
Souza, Max O.
dc.subject.por.fl_str_mv Diffusive limits
Differential equations
SIS epidemiological models
IBM modelling
Differential equations
Diffusive limits
IBM modelling
SIS epidemiological models
topic Diffusive limits
Differential equations
SIS epidemiological models
IBM modelling
Differential equations
Diffusive limits
IBM modelling
SIS epidemiological models
description 550030/2010-7.
publishDate 2014
dc.date.none.fl_str_mv 2014-06
2014-06-01T00:00:00Z
2017-10-30T23:00:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/24759
url http://hdl.handle.net/10362/24759
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1476-945X
PURE: 379760
https://doi.org/10.1016/j.ecocom.2014.01.006
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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