Epidemics from the Eye of the Pathogen

TL;DR

This paper analyzes the stochastic SIR epidemic model in the cumulative cases domain, revealing a universal, simple pattern in outbreak trajectories that can be described by a Gaussian process fluctuating around a deterministic curve.

Contribution

It provides a theoretical framework showing that epidemic outbreaks in the ICC plane follow a universal Gaussian process, simplifying complex models and aiding analysis.

Findings

Outbreaks in the ICC plane follow a Gaussian process.

The model's variance and fluctuations are explicitly quantified.

Real-world data confirms the universality of the ICC pattern.

Abstract

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.