Analysis of a model of bovine brucellosis using singular perturbations

In this paper a model of bovine brucellosis spread is analyzed. This model consider four epidemiological classes: susceptibles, aborting infectious, infectious carriers and immune by vaccination. The per capita death rates of susceptibles, aborting and carriers are interpreted as slaughtering rates and they are time variable in order to maintain the size of the herd constant. A description of the evolution of the disease at the beginning of the epizootiological outbreak is given by means of singular perturbation techniques. We obtain a threshold parameter for the outbreak of the disease and a description of the asymptotic behavior of the model by using a theorem of Markus on asymptotically autonomous systems.