  While a common trend in disease modeling is to develop models of increasing
complexity, it was recently pointed out that outbreaks appear remarkably simple
when viewed in the incidence vs. cumulative cases (ICC) plane. This article
details the theory behind this phenomenon by analyzing the stochastic SIR
(Susceptible, Infected, Recovered) model in the cumulative cases domain. We
prove that the Markov chain associated with this model reduces, in the ICC
plane, to a pure birth chain for the cumulative number of cases, whose limit
leads to an independent increments Gaussian process that fluctuates about a
deterministic ICC curve. We calculate the associated variance and quantify the
additional variability due to estimating incidence over a finite period of
time. We also illustrate the universality brought forth by the ICC concept on
real-world data for Influenza A and for the COVID-19 outbreak in Arizona.
