[Mathematical model of epidemiology of an anthropozoonose: brucellosis (author's transl)]

We are trying to make a model of the epidemiology of Brucellosis by using a two-type branching process. In this text, we are studying the probability of extinction. A complete study on the theory of process with a finite number of types was made by SEVAST'YANOV (1951) [6]. The study of the behaviour of such a process is made with the help of the generating function of the number of infected animals by a single animal. To express this generating function, we start with the same hypothesis as BARTOSZYNSKI [2] (1965) when he makes an interhuman epidemic model by a simple branching process of GALTON-WATSON. However these hypothesis will be modified in order to adapt them to the types of Brucellosis contamination.