Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/76050
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLiu, Ken_US
dc.creatorLou, Yen_US
dc.creatorWu, Jen_US
dc.date.accessioned2018-05-10T02:55:15Z-
dc.date.available2018-05-10T02:55:15Z-
dc.identifier.issn0022-0396en_US
dc.identifier.urihttp://hdl.handle.net/10397/76050-
dc.language.isoenen_US
dc.publisherAcademic Pressen_US
dc.rights© 2017 Elsevier Inc. All rights reserved.en_US
dc.rights© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.rightsThe following publication Liu, K., Lou, Y., & Wu, J. (2017). Analysis of an age structured model for tick populations subject to seasonal effects. Journal of Differential Equations, 263(4), 2078-2112 is available at https://doi.org/10.1016/j.jde.2017.03.038en_US
dc.subjectAge-structureen_US
dc.subjectSeasonal effectsen_US
dc.subjectPeriodic delayen_US
dc.subjectTick populationen_US
dc.subjectUniform persistenceen_US
dc.subjectGlobal stabilityen_US
dc.titleAnalysis of an age structured model for tick populations subject to seasonal effectsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spage2078en_US
dc.identifier.epage2112en_US
dc.identifier.volume263en_US
dc.identifier.issue4en_US
dc.identifier.doi10.1016/j.jde.2017.03.038en_US
dcterms.abstractWe investigate an age-structured hyperbolic equation model by allowing the birth and death functions to be density dependent and periodic in time with the consideration of seasonal effects. By studying the integral form solution of this general hyperbolic equation obtained through the method of integration along characteristics, we give a detailed proof of the uniqueness and existence of the solution in light of the contraction mapping theorem. With additional biologically natural assumptions, using the tick population growth as a motivating example, we derive an age-structured model with time-dependent periodic maturation delays, which is quite different from the existing population models with time-independent maturation delays. For this periodic differential system with seasonal delays, the basic reproduction number R-0 is defined as the spectral radius of the next generation operator. Then, we show the tick population tends to die out when R-0 < 1 while remains persistent if R-0 > 1. When there is no infra-specific competition among immature individuals due to the sufficient availability of immature tick hosts, the global stability of the positive periodic state for the whole model system of four delay differential equations can be obtained with the observation that a scalar subsystem for the adult stage size can be decoupled. The challenge for the proof of such a global stability result can be overcome by introducing a new phase space, based on which, a periodic solution semiflow can be defined which is eventually strongly monotone and strictly subhomogeneous.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationJournal of differential equations, 15 Aug. 2017, v. 263, no. 4, p. 2078-2112en_US
dcterms.isPartOfJournal of differential equationsen_US
dcterms.issued2017-08-15-
dc.identifier.isiWOS:000402582100006-
dc.identifier.eissn1090-2732en_US
dc.identifier.rosgroupid2017003372-
dc.description.ros2017-2018 > Academic research: refereed > Publication in refereed journalen_US
dc.description.validate201805 bcrcen_US
dc.description.oaAccepted Manuscripten_US
dc.identifier.FolderNumberAMA-0474-
dc.description.fundingSourceRGCen_US
dc.description.fundingSourceOthersen_US
dc.description.fundingTextNSFCen_US
dc.description.pubStatusPublisheden_US
dc.identifier.OPUS6736266-
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