A Differential Mathematical Model for Experiments to Determine the Efficacy of Treatments Against the Bean Weevil

Abstract

The article presents a mathematical model for experiments evaluating the effectiveness of diatomaceous earth treatments against the bean weevil, Acanthoscelides obtectus. The proposed mathematical model is of the differential type, inspired by the category of prey-predator models. The system of equations is nonlinear and is solved numerically. A systemic characterization of the bean weevil treatment process is used to describe the model, which uses three functions of time: the number of beans, the pest population, and the amount of diatomaceous earth. The three functions offer users four applications: forecasting, control, formulation of treatment efficacy estimators, and simulation of different types of pest control. The model is built for closed (isolated) experiments typical of laboratories, but this feature makes it extensible to other treatments to combat bean weevils in closed spaces characteristic of the storage of beans in silos.