In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.