An analysis of a mathematical model describing the geographic spread of dengue disease
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | LOCUS Repositório Institucional da UFV |
Texto Completo: | https://doi.org/10.1016/j.jmaa.2016.06.037 http://www.locus.ufv.br/handle/123456789/22082 |
Resumo: | We consider a system of nonlinear partial differential equations corresponding to a generalization of a mathematical model for geographical spreading of dengue disease proposed in the article by Maidana and Yang (2008) [5]. As in that article, the mosquito population is divided into subpopulations: winged form (mature female mosquitoes) and aquatic form (comprising eggs, larvae and pupae); the human population is divided into the subpopulations: susceptible, infected and removed (or immune). On the other hand, differently from the work by Maidana and Yang, who considered just the one dimensional case with constant coefficients, in the present we allow higher spatial dimensions and also parameters depending on space and time. This last generalization is done to cope with possible abiotic effects as variations in temperature, humidity, wind velocity, carrier capacities, and so on; thus, the results hold for more realistic situations. Moreover, we also consider the effects of additional control terms. We perform a rigorous mathematical analysis and present a result on existence and uniqueness of solutions of the problem; furthermore, we obtain estimates of the solution in terms of certain norms of the given parameters of the problem. This kind of result is important for the analysis of optimal control problems with the given dynamics; to exemplify their utility, we also briefly describe how they can be used to show the existence of optimal controls that minimize a given optimality criteria. |
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Araujo, Anderson L. A. deBoldrini, José LuizCalsavara, Bianca Morelli Rodolfo2018-10-01T11:47:27Z2018-10-01T11:47:27Z2016-12-010022-247Xhttps://doi.org/10.1016/j.jmaa.2016.06.037http://www.locus.ufv.br/handle/123456789/22082We consider a system of nonlinear partial differential equations corresponding to a generalization of a mathematical model for geographical spreading of dengue disease proposed in the article by Maidana and Yang (2008) [5]. As in that article, the mosquito population is divided into subpopulations: winged form (mature female mosquitoes) and aquatic form (comprising eggs, larvae and pupae); the human population is divided into the subpopulations: susceptible, infected and removed (or immune). On the other hand, differently from the work by Maidana and Yang, who considered just the one dimensional case with constant coefficients, in the present we allow higher spatial dimensions and also parameters depending on space and time. This last generalization is done to cope with possible abiotic effects as variations in temperature, humidity, wind velocity, carrier capacities, and so on; thus, the results hold for more realistic situations. Moreover, we also consider the effects of additional control terms. We perform a rigorous mathematical analysis and present a result on existence and uniqueness of solutions of the problem; furthermore, we obtain estimates of the solution in terms of certain norms of the given parameters of the problem. This kind of result is important for the analysis of optimal control problems with the given dynamics; to exemplify their utility, we also briefly describe how they can be used to show the existence of optimal controls that minimize a given optimality criteria.engJournal of Mathematical Analysis and ApplicationsVolume 444, Issue 1, Pages 298-325, December 2016Elsevier B. V.info:eu-repo/semantics/openAccessNonlinear systemExistence of solutionsOptimal controlDengueAn analysis of a mathematical model describing the geographic spread of dengue diseaseinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdfTexto completoapplication/pdf561863https://locus.ufv.br//bitstream/123456789/22082/1/artigo.pdfa0f0bcafe5e6610b2bb257e4a1ac8874MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/22082/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILartigo.pdf.jpgartigo.pdf.jpgIM Thumbnailimage/jpeg4770https://locus.ufv.br//bitstream/123456789/22082/3/artigo.pdf.jpgc5dcbe64b036f4fb9925c56f45242b1eMD53123456789/220822018-10-01 23:00:46.494oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-10-02T02:00:46LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false |
dc.title.en.fl_str_mv |
An analysis of a mathematical model describing the geographic spread of dengue disease |
title |
An analysis of a mathematical model describing the geographic spread of dengue disease |
spellingShingle |
An analysis of a mathematical model describing the geographic spread of dengue disease Araujo, Anderson L. A. de Nonlinear system Existence of solutions Optimal control Dengue |
title_short |
An analysis of a mathematical model describing the geographic spread of dengue disease |
title_full |
An analysis of a mathematical model describing the geographic spread of dengue disease |
title_fullStr |
An analysis of a mathematical model describing the geographic spread of dengue disease |
title_full_unstemmed |
An analysis of a mathematical model describing the geographic spread of dengue disease |
title_sort |
An analysis of a mathematical model describing the geographic spread of dengue disease |
author |
Araujo, Anderson L. A. de |
author_facet |
Araujo, Anderson L. A. de Boldrini, José Luiz Calsavara, Bianca Morelli Rodolfo |
author_role |
author |
author2 |
Boldrini, José Luiz Calsavara, Bianca Morelli Rodolfo |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Araujo, Anderson L. A. de Boldrini, José Luiz Calsavara, Bianca Morelli Rodolfo |
dc.subject.pt-BR.fl_str_mv |
Nonlinear system Existence of solutions Optimal control Dengue |
topic |
Nonlinear system Existence of solutions Optimal control Dengue |
description |
We consider a system of nonlinear partial differential equations corresponding to a generalization of a mathematical model for geographical spreading of dengue disease proposed in the article by Maidana and Yang (2008) [5]. As in that article, the mosquito population is divided into subpopulations: winged form (mature female mosquitoes) and aquatic form (comprising eggs, larvae and pupae); the human population is divided into the subpopulations: susceptible, infected and removed (or immune). On the other hand, differently from the work by Maidana and Yang, who considered just the one dimensional case with constant coefficients, in the present we allow higher spatial dimensions and also parameters depending on space and time. This last generalization is done to cope with possible abiotic effects as variations in temperature, humidity, wind velocity, carrier capacities, and so on; thus, the results hold for more realistic situations. Moreover, we also consider the effects of additional control terms. We perform a rigorous mathematical analysis and present a result on existence and uniqueness of solutions of the problem; furthermore, we obtain estimates of the solution in terms of certain norms of the given parameters of the problem. This kind of result is important for the analysis of optimal control problems with the given dynamics; to exemplify their utility, we also briefly describe how they can be used to show the existence of optimal controls that minimize a given optimality criteria. |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-12-01 |
dc.date.accessioned.fl_str_mv |
2018-10-01T11:47:27Z |
dc.date.available.fl_str_mv |
2018-10-01T11:47:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
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article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.1016/j.jmaa.2016.06.037 http://www.locus.ufv.br/handle/123456789/22082 |
dc.identifier.issn.none.fl_str_mv |
0022-247X |
identifier_str_mv |
0022-247X |
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https://doi.org/10.1016/j.jmaa.2016.06.037 http://www.locus.ufv.br/handle/123456789/22082 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.pt-BR.fl_str_mv |
Volume 444, Issue 1, Pages 298-325, December 2016 |
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Elsevier B. V. info:eu-repo/semantics/openAccess |
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Elsevier B. V. |
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openAccess |
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Journal of Mathematical Analysis and Applications |
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Journal of Mathematical Analysis and Applications |
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