The interplay between multiple control mechanisms in a host–parasitoid system: a discrete-time stage-structured modelling approach

Abstract

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 local stability of an interior equilibrium and system persistence. 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.

Keywords:

• Host–parasitoid
• stage structure
• impulsive difference equations
• integrated pest management
• global dynamics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of A. S. Ackleh is supported in part by funds from the R.P. Authement Eminent Scholar and Endowed Chair in Computational Mathematics. The research of A. Veprauskas and J. Jahangir is supported in part by the Louisiana Board of Regents Office of Sponsored Programs RCS Fund, LEQSF(2020-23)-RD-A-28.