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

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.