Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.21/9634 |
Resumo: | Despite 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. |
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Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic modelExplicit solutionsSIR epidemic modelSeasonal fluctuationsChaotic behaviorFlutuações sazonaisComportamento caóticoDespite 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.Springer VerlagRCIPLDuarte, JorgeJanuário, CristinaMartins, NunoRogovchenko, SvitlanaRogovchenko, Yuriy2019-03-06T09:16:49Z2019-062019-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/9634engDUARTE, 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. 2235-22581432-1416https://doi.org/10.1007/s00285-019-01342-7metadata only accessinfo: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:RCAAP2023-08-03T09:58:34Zoai:repositorio.ipl.pt:10400.21/9634Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:18:10.235473Repositório 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 |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
title |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
spellingShingle |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model Duarte, Jorge Explicit solutions SIR epidemic model Seasonal fluctuations Chaotic behavior Flutuações sazonais Comportamento caótico |
title_short |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
title_full |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
title_fullStr |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
title_full_unstemmed |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
title_sort |
Chaos analysis and explicit series solutions to the seasonally forced SIR epidemic model |
author |
Duarte, Jorge |
author_facet |
Duarte, Jorge Januário, Cristina Martins, Nuno Rogovchenko, Svitlana Rogovchenko, Yuriy |
author_role |
author |
author2 |
Januário, Cristina Martins, Nuno Rogovchenko, Svitlana Rogovchenko, Yuriy |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
RCIPL |
dc.contributor.author.fl_str_mv |
Duarte, Jorge Januário, Cristina Martins, Nuno Rogovchenko, Svitlana Rogovchenko, Yuriy |
dc.subject.por.fl_str_mv |
Explicit solutions SIR epidemic model Seasonal fluctuations Chaotic behavior Flutuações sazonais Comportamento caótico |
topic |
Explicit solutions SIR epidemic model Seasonal fluctuations Chaotic behavior Flutuações sazonais Comportamento caótico |
description |
Despite 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. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-03-06T09:16:49Z 2019-06 2019-06-01T00:00:00Z |
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/10400.21/9634 |
url |
http://hdl.handle.net/10400.21/9634 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
DUARTE, 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. 2235-2258 1432-1416 https://doi.org/10.1007/s00285-019-01342-7 |
dc.rights.driver.fl_str_mv |
metadata only access info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
metadata only access |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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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1799133445766512640 |