Recently, our Epidemiological Modeling team published a paper in the American Physical Society’s Physical Review E: statistical, nonlinear, and soft matter physics journal. The paper — Influence of High-order Nonlinear Fluctuations in the Multivariate Susceptible-infectious-recovered Master Equation — details our work with the susecptible-infectious-recovered epidemiological model, which is the canonical model for the propagation of an infectious disease. Since this process is inherently discrete and stochastic, it obeys the so-called Master Equation. Monte Carlo methods are typically used to solve this equation; however, in some instances a power series expansion can be an effective alternative. In this paper the team formulated a hybrid analytical-numerical method, where the Master Equation is expanded and the resultant nonlinear moment equations are assembled analytically, then numerical integration is used to solve the moment equations. The advantage of this method is that the effect of the parameters can be easily analyzed. In this paper the team analyzed two parameters, the reproductive number of the disease and the total population size, and showed that fluctuations in the stochastic process become important as the reproductive number approaches unity. This result is relevant to public health campaigns, which generally deal with the efficacy of a vaccine program, the objective of which is to drive the effective reproduction number close to or below unity so as to eradicate the disease.