Estudo da dinâmica de transmissão da Tuberculose Bovina por meio de equações diferenciais ordinárias.

Abstract

There are diseases that affect the livestock, including the Bovine Tuberculosis, caused by the Mycobacterium bovis bacterium. Such infection affects domestic animals and it’s also transmitted to humans, provoking to the development of programs for the control and/or eradication of Bovine Tuberculosis, and for this, studies are necessary on the transmission dynamics, making use of mathematical models. Thus, the main objective of this work is to analyze a model for Bovine Tuberculosis by means of qualitative theory of Ordinary Differential Equations (ODE). In the qualitative analysis we show the equilibrium points, disease-free and endemic, the basic reproduction ratio R0 is calculated, the local stability of both equilibrium points and the global stability of the point of disease-free equilibrium. We also proposed a model considering constant the human population and non constante the bovine population, showing the equilibrium points, the local stability of equilibrium point disease-free, and basic reproduction ratio R0. Were also performed Numerical simulations in the program Rr (R CORE TEAM, 2018) by adapting the data present in Abakar et al. (2017), where the simulations corroborate with the obtained results, considering different values for the basic reproduction rate. In addition, a simulation was performed with data from brazillian state Rio Grande do Sul.