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dc.contributor.authorBenedito, A. S.
dc.contributor.authorFerreira, C. P.
dc.contributor.authorAdimy, M. [UNESP]
dc.identifier.citationMathematical Modelling of Natural Phenomena, v. 15.
dc.description.abstractStarting 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.en
dc.relation.ispartofMathematical Modelling of Natural Phenomena
dc.subjectAge and stage structured partial differential system
dc.subjectDelay differential system
dc.subjectHopf bifurcation
dc.subjectLocal and global asymptotic stability
dc.titleModeling the dynamics of Wolbachia -infected and uninfected A edes aegypti populations by delay differential equationsen
dc.contributor.institutionUniversité de Lyon
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.description.affiliationInria Université de Lyon, Université Lyon 1
dc.description.affiliationSão Paulo State University (UNESP) Institute of Biosciences
dc.description.affiliationUnespSão Paulo State University (UNESP) Institute of Biosciences
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