Um modelo de ecologia matemática para o controle de pragas com base na dinâmica populacional: estudo de caso no controle da praga da soja

Abstract

The present thesis proposes an alternative approach in the mathematical simulation of a worrisome scenario in ecology: the control of pests harmful to a given soybean crop in a specific geographic region. Modeling of population dynamics is used, where it is studied in an unprecedented way what happens when complementing the ability to predator support the effect that occurs with the increase/decrease of prey. These equations, that model interaction behavior among species present in a medium (such as population dynamics in a predator-prey relationship), have, with the initially used parameters, a break-even with higher levels of pest than desired in the agricultural context under examination. This points to the need of optimal control theory. Coupled to such a system, we have the presence of a nonlinear partial differential equation with the aim to model the fungus dispersion and transport along with its population dynamics through intra-specific competition. The scheme developed in this work leads to sufficiently simple tools, in order to make its hereby use feasible thorough study and analysis in real environments. Data employed to treat the problem that has led to this interdisciplinary research have been collected from bibliographic material edited by Brazilian Agricultural Research Company – EMBRAPA.