Article ID Journal Published Year Pages File Type
5760436 Mathematical Biosciences 2017 25 Pages PDF
Abstract
In this paper, we establish and study a basic stage-structured model for the population of Hyphantria cunea, a delay differential equation model and a model incorporating the resource and seasonality. By introducing the population reproduction number R0, we show that R0 acts as a threshold parameter for the existence and stability of equilibria. The trivial equilibria of the above models are all globally asymptotically stable when R0<1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R0>1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R0>1. Numerical simulations are carried out to illustrate the theoretical results. In addition, we consider the effect of temperature and season on the population of Hyphantria cunea.
Related Topics
Life Sciences Agricultural and Biological Sciences Agricultural and Biological Sciences (General)
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