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Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model

dc.contributor.authorDuarte, Jorge
dc.contributor.authorJanuário, Cristina
dc.contributor.authorMartins, Nuno
dc.contributor.authorRogovchenko, Svitlana
dc.contributor.authorRogovchenko, Yuriy
dc.date.accessioned2019-03-06T09:16:49Z
dc.date.available2019-03-06T09:16:49Z
dc.date.issued2019-06
dc.description.abstractDespite numerous studies of epidemiological systems, the role of seasonality in the recurrent epidemics is not entirely understood. During certain periods of the year incidence rates of a number of endemic infectious diseases may fluctuate dramatically. This influences the dynamics of mathematical models describing the spread of infection and often leads to chaotic oscillations. In this paper, we are concerned with a generalization of a classical Susceptible–Infected–Recovered epidemic model which accounts for seasonal effects. Combining numerical and analytic techniques, we gain new insights into the complex dynamics of a recurrent disease influenced by the seasonality. Computation of the Lyapunov spectrum allows us to identify different chaotic regimes, determine the fractal dimension and estimate the predictability of the appearance of attractors in the system. Applying the homotopy analysis method, we obtain series solutions to the original nonautonomous SIR model with a high level of accuracy and use these approximations to analyze the dynamics of the system. The efficiency of the method is guaranteed by the optimal choice of an auxiliary control parameter which ensures the rapid convergence of the series to the exact solution of the forced SIR epidemic model.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationDUARTE, Jorge; [et al] – Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model. Journal of Mathematical Biology. ISSN 1432-1416. Vol. 78, N.º 7 (2019), pp. 2235-2258pt_PT
dc.identifier.doihttps://doi.org/10.1007/s00285-019-01342-7pt_PT
dc.identifier.issn1432-1416
dc.identifier.issn0303-6812
dc.identifier.urihttp://hdl.handle.net/10400.21/9634
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherSpringer Verlagpt_PT
dc.relation.publisherversionhttps://link.springer.com/content/pdf/10.1007%2Fs00285-019-01342-7.pdfpt_PT
dc.subjectExplicit solutionspt_PT
dc.subjectSIR epidemic modelpt_PT
dc.subjectSeasonal fluctuationspt_PT
dc.subjectChaotic behaviorpt_PT
dc.subjectFlutuações sazonaispt_PT
dc.subjectComportamento caóticopt_PT
dc.titleChaos analysis and explicit series solutions to the seasonally forced SIR epidemic modelpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04106%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04459%2F2013/PT
oaire.citation.endPage2258pt_PT
oaire.citation.issue7
oaire.citation.startPage2235pt_PT
oaire.citation.titleJournal of Mathematical Biologypt_PT
oaire.citation.volume78
oaire.fundingStream5876
oaire.fundingStream5876
person.familyNameDuarte
person.familyNameJanuário
person.familyNameRogovchenko
person.familyNameRogovchenko
person.givenNameJorge
person.givenNameCristina
person.givenNameSvitlana
person.givenNameYuriy
person.identifier.ciencia-idBC1D-1E83-E2B2
person.identifier.ciencia-id101B-390C-E67C
person.identifier.orcid0000-0003-2641-3199
person.identifier.orcid0000-0002-6978-876X
person.identifier.orcid0000-0003-2173-0101
person.identifier.orcid0000-0001-8002-4974
person.identifier.orcid0000-0002-6463-741X
person.identifier.ridG-7261-2011
person.identifier.scopus-author-id35310049800
person.identifier.scopus-author-id56526791400
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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