Mathematical Models for Brown Planthopper Infestation of Rice under Habitat Complexity and Monsoon Effects

Annual Meeting in Mathematics 2023

Abstract

In this research, we study mathematical predator-prey models for brown planthopper (BPH) infestation of rice under the effects of habitat complexity and monsoon for two time scales. Using a fast time scale, we obtain a complete model which is a system of first-order differential equations including logistic growth terms, modified Holling type II functional responses and migration terms due to the monsoon. The positivity and boundedness of the fast time-scale model are proved. Using a slow time scale and the aggregated method, we obtain an aggregated model which is less complicated than the former model in terms of the number of variables and parameters. We investigate the existence of equilibrium points and their local asymptotic stability for this aggregrated model. Hopf bifurcation of the aggregrated model is also shown to occur as the maximum carrying capacity is varied. Numerical simulations are performed to illustrate the theoretical results. Finally, some ecological discussion of methods for reducing the BPH dispersion of the model is given.