Modeling Insights from COVID-19 Incidence Data: Part II -- Why are compartment models so accurate?

TL;DR

This paper explains why the simple SIR compartment model accurately fits COVID-19 data despite population heterogeneity, by mathematically demonstrating its approximation to more complex models with contact heterogeneity.

Contribution

It provides a mathematical analysis showing the SIR model's close approximation to heterogeneous contact models and offers insights into interpreting model parameters.

Findings

SIR model fits real data well despite heterogeneity.

Mathematical demonstration of the approximation.

Guidance on interpreting parameters from regression.

Abstract

The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although real populations have heterogeneities in contacts not represented in the SIR model, it nevertheless well fits real U.S. state data at multiple points throughout the pandemic. Here we demonstrate mathematically how closely the simple continuous SIR model approximates a model which includes heterogeneous contacts, and provide insight onto how one can interpret parameters gleaned from regression in the context of heterogeneous dynamics.