Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/76050
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Liu, K | en_US |
dc.creator | Lou, Y | en_US |
dc.creator | Wu, J | en_US |
dc.date.accessioned | 2018-05-10T02:55:15Z | - |
dc.date.available | 2018-05-10T02:55:15Z | - |
dc.identifier.issn | 0022-0396 | en_US |
dc.identifier.uri | http://hdl.handle.net/10397/76050 | - |
dc.language.iso | en | en_US |
dc.publisher | Academic Press | en_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.rights | The 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.2017.03.038 | en_US |
dc.subject | Age-structure | en_US |
dc.subject | Seasonal effects | en_US |
dc.subject | Periodic delay | en_US |
dc.subject | Tick population | en_US |
dc.subject | Uniform persistence | en_US |
dc.subject | Global stability | en_US |
dc.title | Analysis of an age structured model for tick populations subject to seasonal effects | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.spage | 2078 | en_US |
dc.identifier.epage | 2112 | en_US |
dc.identifier.volume | 263 | en_US |
dc.identifier.issue | 4 | en_US |
dc.identifier.doi | 10.1016/j.jde.2017.03.038 | en_US |
dcterms.abstract | We 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.accessRights | open access | en_US |
dcterms.bibliographicCitation | Journal of differential equations, 15 Aug. 2017, v. 263, no. 4, p. 2078-2112 | en_US |
dcterms.isPartOf | Journal of differential equations | en_US |
dcterms.issued | 2017-08-15 | - |
dc.identifier.isi | WOS:000402582100006 | - |
dc.identifier.eissn | 1090-2732 | en_US |
dc.identifier.rosgroupid | 2017003372 | - |
dc.description.ros | 2017-2018 > Academic research: refereed > Publication in refereed journal | en_US |
dc.description.validate | 201805 bcrc | en_US |
dc.description.oa | Accepted Manuscript | en_US |
dc.identifier.FolderNumber | AMA-0474 | - |
dc.description.fundingSource | RGC | en_US |
dc.description.fundingSource | Others | en_US |
dc.description.fundingText | NSFC | en_US |
dc.description.pubStatus | Published | en_US |
dc.identifier.OPUS | 6736266 | - |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
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Liu_Analysis_Age_Structured.pdf | Pre-Published version | 1.01 MB | Adobe PDF | View/Open |
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