Lu Haixia, Song Haitao, Zhu Huaiping
School of Arts and Science, Suqian College, Suqian, Jiangsu, 223800, PR China; Laboratory of Mathematical Parallel Systems (Lamps), Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada.
Laboratory of Mathematical Parallel Systems (Lamps), Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada; Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, 030006, PR China.
Math Biosci. 2017 Oct;292:57-66. doi: 10.1016/j.mbs.2017.07.010. Epub 2017 Jul 19.
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, we show that R 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<1; the basic model and the delay-differential model have a unique positive equilibrium respectively, and they are both locally asymptotically stable when R>1; the model with periodic season is uniformly persistent and admits a positive periodic solution if R>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.
在本文中，我们建立并研究了美国白蛾种群的一个基本阶段结构模型、一个时滞微分方程模型以及一个包含资源和季节性的模型。通过引入种群繁殖数(R)，我们表明(R)作为平衡点存在性和稳定性的阈值参数。当(R\lt1)时，上述模型的平凡平衡点都是全局渐近稳定的；基本模型和时滞微分模型分别有唯一的正平衡点，当(R\gt1)时它们都是局部渐近稳定的；具有周期性季节的模型如果(R\gt1)则是一致持久的并且存在一个正周期解。进行了数值模拟以说明理论结果。此外，我们考虑了温度和季节对美国白蛾种群的影响。
