Um estudo das doenças Brucelose e Babesiose bovina com população não constante

Abstract

Livestock farming has a great relevance in the Brazilian economy. It is an economic activity developed in rural areas that consists of the cattle raising with the purpose of commercializing them, thus supplying the needs of the breeder. Several diseases can affect livestock, among them the infectious diseases Babesiosis and Brucellosis, both bovines. Therefore, there is concern about the control of these diseases due to the importance of cattle raising for the economy. Thus researchers began to use mathematical modeling to describe the dynamics of these diseases, in order to seek their control. The objective of this work is to generalize the model for Babesiosis that involves ordinary differences equations, using the non constant population of ticks. For this, the Qualitative Theory of Ordinary Differential Equations is used. We developed two models with non constant population of ticks and showed the equilibrium points, basic reproduction ratio and stability analysis. Also the numerical simulation of the studied models was carried out displaying graphs to analyze the behavior of the populations over time.