MODEL PREDATOR-PREY DENGAN KONTROL OPTIMAL PADA BUDIDAYA BAWANG MERAH

Abstract

Shallot farming creates a predator–prey interaction between leaf miner flies as pests and pesticides as control agents applied by farmers. This article discusses the application of a predator–prey mathematical model to shallot cultivation in Selopamioro Village, Imogiri, Bantul. The interaction between predator and prey is mathematically formulated using the Holling-Tanner response function and analyzed numerically using the fourth-order Runge-Kutta method to examine equilibrium point stability. The model is further developed by introducing optimal control in the form of manual pest removal and reduced insecticide dosage, aiming to improve shallot productivity through more effective pest management. The state and co-state conditions are solved using the Forward–Backward Sweep method based on the fourth-order Runge-Kutta on the Hamiltonian function. Simulation results show that the implementation of control significantly reduces the leaf miner fly population from 997 to 141 individuals and decreases the duration of insecticide application from 39 days to just 10 days