A Theoretical Approach to Understanding Population Dynamics with Seasonal Developmental Durations

Yijun Lou, Xiao Qiang Zhao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)573-603
Number of pages31
JournalJournal of Nonlinear Science
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017

Keywords

  • Basic reproduction ratio
  • Functional differential equation
  • Host-parasite interaction
  • Periodic delay
  • Seasonal developmental duration
  • Threshold dynamics

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

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