From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations

Detalhes bibliográficos
Autor(a) principal: Esquível, Manuel Leote
Data de Publicação: 2020
Outros Autores: Patrício, Paula Cristiana Costa Garcia da Silva, Guerreiro, Gracinda Rita Diogo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/116904
Resumo: UID/MAT/00297/2020
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spelling From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populationsInfection modelingpopulation dynamicsOrdinary differentila equationsStochastic differential equationsMarkov chainsUID/MAT/00297/2020We present a methodology to connect an ordinary dierential equation (ODE) model of interacting entities at the individual level, to an open Markov chain (OMC) model of a population of such individuals, via a stochastic diferential equation (SDE) intermediate model. The ODE model here presented is formulated as a dynamic change between two regimes; one regime is of mean reverting type and the other is of inverse logistic type. For the general purpose of defining an OMC model for a population of individuals, we associate an Ito processes, in the form of SDE to ODE system of equations, by means of the addition of Gaussian noise terms which may be thought to model non essential characteristics of the phenomena with small and undifferentiated influences. The next step consists on discretizing the SDE and using the discretized trajectories computed by simulation to define transitions of a finite valued Markov chain; for that, the state space of the Ito processes is partitioned according to some rule. For the example proposed for illustration, the state space of the ODE system referred – corresponding to a model of a viral infection – is partitioned into six infection classes determined by some of the critical points of the ODE system; we detail the evolution of some infected population in these infection classes.DM - Departamento de MatemáticaCMA - Centro de Matemática e AplicaçõesRUNEsquível, Manuel LeotePatrício, Paula Cristiana Costa Garcia da SilvaGuerreiro, Gracinda Rita Diogo2021-05-03T22:55:25Z2020-12-172020-12-17T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article18application/pdfhttp://hdl.handle.net/10362/116904eng2544-7297PURE: 28937966https://doi.org/10.1515/cmb-2020-0110info: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:RCAAP2024-03-11T04:59:47Zoai:run.unl.pt:10362/116904Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:43:21.874958Repositório 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 From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
title From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
spellingShingle From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
Esquível, Manuel Leote
Infection modeling
population dynamics
Ordinary differentila equations
Stochastic differential equations
Markov chains
title_short From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
title_full From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
title_fullStr From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
title_full_unstemmed From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
title_sort From ODE to Open Markov Chains, via SDE: an application to models for infections in individuals and populations
author Esquível, Manuel Leote
author_facet Esquível, Manuel Leote
Patrício, Paula Cristiana Costa Garcia da Silva
Guerreiro, Gracinda Rita Diogo
author_role author
author2 Patrício, Paula Cristiana Costa Garcia da Silva
Guerreiro, Gracinda Rita Diogo
author2_role author
author
dc.contributor.none.fl_str_mv DM - Departamento de Matemática
CMA - Centro de Matemática e Aplicações
RUN
dc.contributor.author.fl_str_mv Esquível, Manuel Leote
Patrício, Paula Cristiana Costa Garcia da Silva
Guerreiro, Gracinda Rita Diogo
dc.subject.por.fl_str_mv Infection modeling
population dynamics
Ordinary differentila equations
Stochastic differential equations
Markov chains
topic Infection modeling
population dynamics
Ordinary differentila equations
Stochastic differential equations
Markov chains
description UID/MAT/00297/2020
publishDate 2020
dc.date.none.fl_str_mv 2020-12-17
2020-12-17T00:00:00Z
2021-05-03T22:55:25Z
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/10362/116904
url http://hdl.handle.net/10362/116904
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2544-7297
PURE: 28937966
https://doi.org/10.1515/cmb-2020-0110
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 18
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
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instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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