Grid Sensitivity Studies for Single and Multi-Step Ice Accretion using Unstructured Meshes

One insect pest that causes enormous damage to rice plants in many countires is the brown planthopper (BPH). Various strategies have been proposed to control BPH outbreaks, such as cultural control, physical control, chemical control and biological control. Integrated pest management (IPM) is a method of controlling pests using a variety of methods to achieve effective and environmentally friendly results. However, the best methods in IPM application are yet to be determined. Since laboratory experiments have limitations in many respects, such as ethics, time, environment, and cost, mathematical modeling is considered as an option which can be used to study the effects of IPM on BPH infestation. In this article, we investigate mathematical models describing management of BPH under IPM strategies. In particular, we study two biological control agents including Cyrtorhinus lividipennis, a natural enemy of BPH, and Metarhizium neoanisopliae, an entomopathogenic fungus that causes diseases in pests. A data set from laboratory experiments previously published is also used in this study. In addition, we study functional responses describing predator's prey consumption. Finally, mathematical features of the proposed models are analyzed. The existence of equilibrium points, their stability and Hopf bifurcation are proved and numerical results are obtained to illustrate the theoretical results. This study suggests that using IPM is an effective method for rapidly reducing insect populations in the early stages of BPH outbreaks which might contribute to the long-term suppression of BPH.