"A discrete time stage structured host parasitoid model with pest control."
We propose a discrete-time host-parasitoid model with stage structure in both species. For this model, we establish conditions for the existence and global stability of the extinction and parasitoid-free equilibria as well as conditions for the existence and uniqueness of an interior equilibrium. We study the model numerically to examine how pesticide spraying may interact with natural enemies (parasitoids) to control the pest (host) species. We then extend the model to an impulsive difference system that incorporates both periodic pesticide spraying and augmentation of the natural enemies to suppress the pest population. For this system we determine when the pest-eradication periodic solution is globally attracting. We also examine how varying the control measures (pesticide concentration, natural enemy augmentation, and the frequency of applications) may lead to different pest outbreak or persistence outcomes when eradication does not occur.
Additional authors: Azmy Ackleh; Amy Veprauskas.