Introduction to epidemic modeling is usually made through one of the first epidemic models proposed by Kermack and McKendrick in 1927, a model known as the SIR epidemic model and by ignoring the hypotheses of the model SIR, we arrive at the complicated SIS and SIR models with demography. In these models, we saw that the most basic SIR epidemic model has a unique endemic equilibrium, which is globally stable if R0 gt; 1. This means that every solution converges to a stationary state. On the other hand, many times, the incidence or the prevalence data of various diseases exhibit periodicity. To illustrate the application of the Hopf bifurcation theorem, we consider a simple modification of the SIR model. Assume that the transmission coefficient of infection is not constant but linear in the number of diseases.