Population dynamics of fungi that cause stem diseases in vines under the action of possible inhibitory agents

Abstract

The article introduces mathematical contributions for the areas of agriculture and phytopathology using actual data and molding the behavior of physical phenomena. The purpose of the work was molding the growth of Botryosphaeria dothidea in culture medium with different components, comparing the experimental data with the classical mathematical model of Verhulst. The experiment was made in the Phytopathology Laboratory – IFRS/Campus Bento Gonçalves, where the culture medium Potato Dextrose Agar (PDA) was prepared with different components that possibly inhibiting growth, besides evidence (exclusively with PDA). The culture medium was allocated in Petri plates and next the fungus Botryosphaeria dothidea was cut up in the center of the plates about this medium. Fungal growth measurements were executed every 12 hours. For the numerical processing and display graphics were used computer software, such as Excel and Scilab. Through Mathematical Models, that consequently reflect in Ordinary Differential Equations, numerical simulations were possible to program, so verifying that the witness showed the smallest mistake in relation to the classical model. It is possible to declare that the fungus growth follows a classical mathematical model (Verhulst). However, it was possible to verify that the culture media that presented possible inhibitors in their composition delayed the growth of the fungus, showing that in this type of situation the classic mathematical model does not describe reality accurately, needing to be adapted.