Similarities exist between rumor propagation and disease spreading. In analogy with the SIR (Susceptible-InfectedRemoved) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor model has been developed. Here, the SIR model was modified with the new compartment, originating the ISSV (Ignorant-Spreader-Stifler-Verifier) rumor model. In this work, the model is presented and how its parameters are related to network characteristics is explained. This paper presents a system of differential equations that describes the spreading of a rumor in a new model, with a novel compartment, the verifier. By using concepts from Dynamical Systems Theory, equilibrium point is calculated, the stability and bifurcation conditions are derived. According parameters and initial conditions, the model is validated with numerical experiments. The relations among the model parameters in the several bifurcation conditions allow a rumor propagation design minimizing risks