An analysis of a mathematical model describing the geographic spread of dengue disease

Detalhes bibliográficos
Autor(a) principal: Araujo, Anderson L. A. de
Data de Publicação: 2016
Outros Autores: Boldrini, José Luiz, Calsavara, Bianca Morelli Rodolfo
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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spelling 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. 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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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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
url 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
dc.rights.driver.fl_str_mv Elsevier B. V.
info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv Journal of Mathematical Analysis and Applications
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