Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/241048 |
Resumo: | We derive a generalized Hamiltonian formalism for a modified suscepti ble–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV model is shown to admit three possible functionally independent Hamiltonians and hence three associated Poisson structures. The reduced case of vanishing vaccinated sector shows a complete correspondence with the known Poisson structures of the SIR model. The SIRV model is shown to be expressible as an almost Nambu sys tem, except for a scale factor function breaking the divergenceless property. In the autonomous case with time-independent stationary ratios k and b, the SIRV model is shown to be a maximally super-integrable system. For this case we test the accuracy of numerical schemes that are suited to solve the stiff set of SIRV differential equations. |
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Haas, FernandoKröger, MartinSchlickeiser, Reinhard2022-06-25T05:03:29Z20221751-8113http://hdl.handle.net/10183/241048001142950We derive a generalized Hamiltonian formalism for a modified suscepti ble–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV model is shown to admit three possible functionally independent Hamiltonians and hence three associated Poisson structures. The reduced case of vanishing vaccinated sector shows a complete correspondence with the known Poisson structures of the SIR model. The SIRV model is shown to be expressible as an almost Nambu sys tem, except for a scale factor function breaking the divergenceless property. In the autonomous case with time-independent stationary ratios k and b, the SIRV model is shown to be a maximally super-integrable system. For this case we test the accuracy of numerical schemes that are suited to solve the stiff set of SIRV differential equations.application/pdfengJournal of physics. A, Mathematical and theoretical. Bristol. Vol. 55, no. 22 (June 2022), 225206, 17 p.Modelos epidemiológicosSistemas hamiltonianosEquações diferenciais ordináriasCorona virusPoisson structureSuper-integrable systemEpidemicsNambu mechanicsCovid-19Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solversEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001142950.pdf.txt001142950.pdf.txtExtracted Texttext/plain40810http://www.lume.ufrgs.br/bitstream/10183/241048/2/001142950.pdf.txtbb8ea651cfa7c1cb8e31d428578b9a98MD52ORIGINAL001142950.pdfTexto completo (inglês)application/pdf1291813http://www.lume.ufrgs.br/bitstream/10183/241048/1/001142950.pdf7a7a88e34a034dd2292fa81a325f98f7MD5110183/2410482023-07-20 03:35:32.05247oai:www.lume.ufrgs.br:10183/241048Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-07-20T06:35:32Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
title |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
spellingShingle |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers Haas, Fernando Modelos epidemiológicos Sistemas hamiltonianos Equações diferenciais ordinárias Corona virus Poisson structure Super-integrable system Epidemics Nambu mechanics Covid-19 |
title_short |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
title_full |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
title_fullStr |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
title_full_unstemmed |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
title_sort |
Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers |
author |
Haas, Fernando |
author_facet |
Haas, Fernando Kröger, Martin Schlickeiser, Reinhard |
author_role |
author |
author2 |
Kröger, Martin Schlickeiser, Reinhard |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Haas, Fernando Kröger, Martin Schlickeiser, Reinhard |
dc.subject.por.fl_str_mv |
Modelos epidemiológicos Sistemas hamiltonianos Equações diferenciais ordinárias |
topic |
Modelos epidemiológicos Sistemas hamiltonianos Equações diferenciais ordinárias Corona virus Poisson structure Super-integrable system Epidemics Nambu mechanics Covid-19 |
dc.subject.eng.fl_str_mv |
Corona virus Poisson structure Super-integrable system Epidemics Nambu mechanics Covid-19 |
description |
We derive a generalized Hamiltonian formalism for a modified suscepti ble–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting SIRV model is shown to admit three possible functionally independent Hamiltonians and hence three associated Poisson structures. The reduced case of vanishing vaccinated sector shows a complete correspondence with the known Poisson structures of the SIR model. The SIRV model is shown to be expressible as an almost Nambu sys tem, except for a scale factor function breaking the divergenceless property. In the autonomous case with time-independent stationary ratios k and b, the SIRV model is shown to be a maximally super-integrable system. For this case we test the accuracy of numerical schemes that are suited to solve the stiff set of SIRV differential equations. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-06-25T05:03:29Z |
dc.date.issued.fl_str_mv |
2022 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/241048 |
dc.identifier.issn.pt_BR.fl_str_mv |
1751-8113 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001142950 |
identifier_str_mv |
1751-8113 001142950 |
url |
http://hdl.handle.net/10183/241048 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Journal of physics. A, Mathematical and theoretical. Bristol. Vol. 55, no. 22 (June 2022), 225206, 17 p. |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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