Analysis of the Predator-Prey Model for False Whitehead (Cnaphalocrosis medinalis) Pests and Rice (Oryza sativa L.) with Holling Type II Response Function and Constant Harvesting on the Prey

Mathematics and Statistics Department, Faculty of Mathematics and Natural Sciences, Universitas Papua, Jalan Gunung Salju, Manokwari, 98314, Papua Barat, Indonesia

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Abstract

False whitehead (Cnaphalocrosis medinalis) infestation in rice (Oryza sativa L.) is one of the main factors that cause a decline in agricultural productivity. This research aims to build and analyze a predator-prey mathematical model that describes the interaction between rice as prey and the false white grub as a predator, considering the Holling Type II response function and constant harvesting strategy on the prey. The model is constructed in the form of a system of differential equations, which are then nondimensionalized to simplify the analysis process. Next, a stability analysis was conducted on the equilibrium points with and without harvesting. The results showed that in the model without harvesting, there were two stable equilibrium points that allowed for coexistence between the two species. In the model with harvesting at certain intervals, a stable positive equilibrium point was obtained. This finding is supported by numerical simulations showing that the dynamics of the system depend on the values of the biological parameters and harvesting rate. The conclusion of this study is that controlled harvesting strategies can maintain a population balance between rice and pests and provide a theoretical basis for sustainable agricultural management based on a mathematical approach.