A series of population models for Hyphantria cunea with delay and seasonality

作者：Lu, Haixia; Song, Haitao; Zhu, Huaiping^*

来源：Mathematical Biosciences, 2017, 292: 57-66.

DOI：10.1016/j.mbs.2017.07.010

• Hyphantria cunea
• Stage-structured population model
• Time delay
• Seasonality
• Population reproduction ratio
• Periodic solution
• Uniform persistence

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 R-0, we show that R-0 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 R-0 < 1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R-0 > 1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R-0 > 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.

• 出版日期2017-10
• 单位宿迁学院; 山西大学