ANÁLISE MATEMÁTICA DO MODELO DE INTERAÇÃO ENTRE A BROCA DA CANA DE AÇUCAR (DIATRAEA SACCHARALIS) E O SEU PARASITOIDE TRICHOGRAMMA GALLOI

The sugarcane borer (Diatraea Saccharalis) is considered the main pest in the sugarcane crop due to the great damage it causes to the crop. Its permanence can portray significant losses in productivity and affect the quality of sugar and ethanol production. One of the methods used to manage the borer is through biological control through the insertion of the parasitoid Trichogramma Galloi. Mathematical modeling helps to understand biological control, as it allows us to carry out a qualitative analysis. In this article, we analyze a mathematical model, based on systems of ordinary differential equations, of the interaction between the sugarcane borer, which is represented by the egg and larval stages, and its parasitoid, which is considered in terms of parasitized eggs. In this model, we find equilibrium points and conditions for the stability of each one of them. Numerical simulations show a good approximation for stability.