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Title: A theoretical approach to understanding population dynamics with seasonal developmental durations
Authors: Lou, Y 
Zhao, XQ
Issue Date: Apr-2017
Source: Journal of nonlinear science, Apr. 2017, v. 27, no. 2, p. 573-603
Abstract: There is a growing body of biological investigations to understand impacts of seasonally changing environmental conditions on population dynamics in various research fields such as single population growth and disease transmission. On the other side, understanding the population dynamics subject to seasonally changing weather conditions plays a fundamental role in predicting the trends of population patterns and disease transmission risks under the scenarios of climate change. With the host–macroparasite interaction as a motivating example, we propose a synthesized approach for investigating the population dynamics subject to seasonal environmental variations from theoretical point of view, where the model development, basic reproduction ratio formulation and computation, and rigorous mathematical analysis are involved. The resultant model with periodic delay presents a novel term related to the rate of change of the developmental duration, bringing new challenges to dynamics analysis. By investigating a periodic semiflow on a suitably chosen phase space, the global dynamics of a threshold type is established: all solutions either go to zero when basic reproduction ratio is less than one, or stabilize at a positive periodic state when the reproduction ratio is greater than one. The synthesized approach developed here is applicable to broader contexts of investigating biological systems with seasonal developmental durations.
Keywords: Basic reproduction ratio
Functional differential equation
Host-parasite interaction
Periodic delay
Seasonal developmental duration
Threshold dynamics
Publisher: Springer
Journal: Journal of nonlinear science 
ISSN: 0938-8974
EISSN: 1432-1467
DOI: 10.1007/s00332-016-9344-3
Rights: © Springer Science+Business Media New York 2016
This is a post-peer-review, pre-copyedit version of an article published in Journal of nonlinear science. The final authenticated version is available online at:
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