Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1051/mmnp/2020041 http://hdl.handle.net/11449/205608 |
Resumo: | Starting from an age structured partial differential model, constructed taking into account the mosquito life cycle and the main features of the Wolbachia-infection, we derived a delay differential model using the method of characteristics, to study the colonization and persistence of the Wolbachia-transinfected Aedes aegypti mosquito in an environment where the uninfected wild mosquito population is already established. Under some conditions, the model can be reduced to a Nicholson-type delay differential system; here, the delay represents the duration of mosquito immature phase that comprises egg, larva and pupa. In addition to mortality and oviposition rates characteristic of the life cycle of the mosquito, other biological features such as cytoplasmic incompatibility, bacterial inheritance, and deviation on sex ratio are considered in the model. The model presents three equilibriums: the extinction of both populations, the extinction of Wolbachia-infected population and persistence of uninfected one, and the coexistence. The conditions of existence for each equilibrium are obtained analytically and have been interpreted biologically. It is shown that the increase of the delay can promote, through Hopf bifurcation, stability switch towards instability for the nonzero equilibriums. Overall, when the delay increases and crosses predetermined thresholds, the populations go to extinction. |
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Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equationsAge and stage structured partial differential systemDelay differential systemHopf bifurcationLocal and global asymptotic stabilityStarting from an age structured partial differential model, constructed taking into account the mosquito life cycle and the main features of the Wolbachia-infection, we derived a delay differential model using the method of characteristics, to study the colonization and persistence of the Wolbachia-transinfected Aedes aegypti mosquito in an environment where the uninfected wild mosquito population is already established. Under some conditions, the model can be reduced to a Nicholson-type delay differential system; here, the delay represents the duration of mosquito immature phase that comprises egg, larva and pupa. In addition to mortality and oviposition rates characteristic of the life cycle of the mosquito, other biological features such as cytoplasmic incompatibility, bacterial inheritance, and deviation on sex ratio are considered in the model. The model presents three equilibriums: the extinction of both populations, the extinction of Wolbachia-infected population and persistence of uninfected one, and the coexistence. The conditions of existence for each equilibrium are obtained analytically and have been interpreted biologically. It is shown that the increase of the delay can promote, through Hopf bifurcation, stability switch towards instability for the nonzero equilibriums. Overall, when the delay increases and crosses predetermined thresholds, the populations go to extinction.Inria Université de Lyon, Université Lyon 1São Paulo State University (UNESP) Institute of BiosciencesSão Paulo State University (UNESP) Institute of BiosciencesUniversité de LyonUniversidade Estadual Paulista (Unesp)Benedito, A. S.Ferreira, C. P.Adimy, M. [UNESP]2021-06-25T10:18:18Z2021-06-25T10:18:18Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1051/mmnp/2020041Mathematical Modelling of Natural Phenomena, v. 15.1760-61010973-5348http://hdl.handle.net/11449/20560810.1051/mmnp/20200412-s2.0-8509788268120527496982046170000-0002-9404-6098Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematical Modelling of Natural Phenomenainfo:eu-repo/semantics/openAccess2021-11-18T17:10:12Zoai:repositorio.unesp.br:11449/205608Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:27:54.112865Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
title |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
spellingShingle |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations Benedito, A. S. Age and stage structured partial differential system Delay differential system Hopf bifurcation Local and global asymptotic stability |
title_short |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
title_full |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
title_fullStr |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
title_full_unstemmed |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
title_sort |
Modeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equations |
author |
Benedito, A. S. |
author_facet |
Benedito, A. S. Ferreira, C. P. Adimy, M. [UNESP] |
author_role |
author |
author2 |
Ferreira, C. P. Adimy, M. [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Université de Lyon Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Benedito, A. S. Ferreira, C. P. Adimy, M. [UNESP] |
dc.subject.por.fl_str_mv |
Age and stage structured partial differential system Delay differential system Hopf bifurcation Local and global asymptotic stability |
topic |
Age and stage structured partial differential system Delay differential system Hopf bifurcation Local and global asymptotic stability |
description |
Starting from an age structured partial differential model, constructed taking into account the mosquito life cycle and the main features of the Wolbachia-infection, we derived a delay differential model using the method of characteristics, to study the colonization and persistence of the Wolbachia-transinfected Aedes aegypti mosquito in an environment where the uninfected wild mosquito population is already established. Under some conditions, the model can be reduced to a Nicholson-type delay differential system; here, the delay represents the duration of mosquito immature phase that comprises egg, larva and pupa. In addition to mortality and oviposition rates characteristic of the life cycle of the mosquito, other biological features such as cytoplasmic incompatibility, bacterial inheritance, and deviation on sex ratio are considered in the model. The model presents three equilibriums: the extinction of both populations, the extinction of Wolbachia-infected population and persistence of uninfected one, and the coexistence. The conditions of existence for each equilibrium are obtained analytically and have been interpreted biologically. It is shown that the increase of the delay can promote, through Hopf bifurcation, stability switch towards instability for the nonzero equilibriums. Overall, when the delay increases and crosses predetermined thresholds, the populations go to extinction. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01-01 2021-06-25T10:18:18Z 2021-06-25T10:18:18Z |
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://dx.doi.org/10.1051/mmnp/2020041 Mathematical Modelling of Natural Phenomena, v. 15. 1760-6101 0973-5348 http://hdl.handle.net/11449/205608 10.1051/mmnp/2020041 2-s2.0-85097882681 2052749698204617 0000-0002-9404-6098 |
url |
http://dx.doi.org/10.1051/mmnp/2020041 http://hdl.handle.net/11449/205608 |
identifier_str_mv |
Mathematical Modelling of Natural Phenomena, v. 15. 1760-6101 0973-5348 10.1051/mmnp/2020041 2-s2.0-85097882681 2052749698204617 0000-0002-9404-6098 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Mathematical Modelling of Natural Phenomena |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129072704782336 |