Dynamics of a pest management model with mate‐finding Allee effect induced by sterile release

Abstract

Using sterile insect release to guide the occurrence of the mate-finding Allee effect in pest populations is considered a pest management strategy. In this paper, a pest management model is established with the mate-finding Allee effect induced by releasing sterile pests. In addition, the natural enemies of pests and spraying insecticide are also taken into account to achieve integrated pest management. For the model without delay, although the origin is not well-defined in our model, we pay attention to the dynamics near the origin and find it is always an attractor. This means the extinction of pests is closely related to their initial scale. Based on that, we conduct a detailed qualitative study on other equilibria. Furthermore, the model with a time delay is also observed. The stability of equilibrium points, Hopf bifurcation, and Bogdanov-Takens bifurcation are all carried out. Through numerical simulation, the results indicate that adding the mate-finding Allee effect can significantly reduce the demand for pesticides and reduce the environmental damage from pesticides, comparing with the traditional approach (i.e., combining natural enemies and pesticides).We also find that a time delay can switch the stability of the equilibrium points and promote the extinction of pests.