In this talk, I will introduce the “cumulative-cases, incidence” (ICC) curve as a phase-plane perspective on the traditional SIR compartmental epidemic model. Through a stochastic representation of this dynamical system, we will uncover statistical properties that appear only in the ICC perspective. I have leveraged these to develop an algorithm that not only fits ICC curves through real data, but also detects change-points and peaks. This will allow us to identify when the epidemic trajectory has changed and quantifying said change.