Please use this identifier to cite or link to this item:
Title: Analysis of an age structured model for tick populations subject to seasonal effects
Authors: Liu, KH 
Lou, YJ 
Wu, JH
Keywords: Age-structure
Seasonal effects
Periodic delay
Tick population
Uniform persistence
Global stability
Issue Date: 15-Aug-2017
Publisher: Academic Press
Source: Journal of differential equations, 2017, v. 263, no. 4, p. 2078-2112 How to cite?
Journal: Journal of differential equations 
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.
ISSN: 0022-0396
EISSN: 1090-2732
DOI: 10.1016/j.jde.2017.03.038
Appears in Collections:Journal/Magazine Article

View full-text via PolyU eLinks SFX Query
Show full item record


Last Week
Last month
Citations as of Dec 13, 2018


Last Week
Last month
Citations as of Dec 13, 2018

Page view(s)

Last Week
Last month
Citations as of Dec 16, 2018

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.