Host-Parasitoid Dynamics and Biological Control of the Sugarcane Borer
We investigate biological pest control strategies for the sugarcane borer Diatraea saccharalis through the combined action of two parasitoid species: the egg parasitoid Trichogramma galloi and the larval parasitoid Cotesia flavipes. We describe the population dynamics with a six-dimensional host-parasitoid model in which host-parasitoid interactions are represented through a Holling Type II functional response, extending previous models by coupling egg and larval stage dynamics and incorporating parasitism saturation observed in laboratory experiments. We characterize the equilibrium structure of the model and analyze the local stability of the extinction equilibrium. Bifurcation analysis reveals that, for a wide range of Holling parameters, the pest population exceeds the economic damage threshold, motivating the design of active control strategies. We formulate and compare three biological control approaches: open-loop optimal control, State-Dependent Riccati Equation (SDRE) feedback control, and impulsive feedback control based on Lyapunov arguments. We perform numerical simulations to show that all three strategies successfully keep the pest population below the economic damage threshold. The impulsive strategy, in particular, achieves effective suppression with substantially fewer parasitoid releases than the continuous approaches, making it the most practically viable option for field implementation.