Dynamics and biological control of the sugarcane borer with two parasitoids

The purpose of this work is to study an interaction between the sugarcane borer and its parasitoids (Trichogramma galloi, and Cotesia flavipes). The interaction between these populations is modeled by a host-parasitoid system considering six ordinary differential equations. The purpose of mathematical modeling is to answer two important issues: Is it possible to control the sugarcane pest only with the egg parasitoid or the larvae parasitoid, or do you need both? Among the control methodologies analyzed in this work, which could be the most appropriate for pest management? Three control methodologies are proposed, continuous control, impulsive control, and the coupling of these two controls, continuous and impulsive. Computer simulations are provided and their results discussed.