Understanding why there are multiple equilibrium points when R 0 < 1 has been one of the main motivations to analyze existence of a backward bifurcation in epidemiological models.Existence of multiple endemic states is usually associated to branches of equilibrium points of the models, which could arise from either the disease-free equilibrium point if R 0 = 1 or from an endemic equilibrium point if R 0 > 1.In this work, an SIR model with a density-dependent treatment rate is analyzed.The nature of the point where backward bifurcation emerges is explained in function of the velocity of the per-capita treatment rate.Strategies for the control or eradication of the disease will be proposed in function of the efficiency of the treatment.