Edge-based compartmental modeling for epidemic spread Part II: Model Selection and Hierarchies

TL;DR

This paper develops a hierarchy of edge-based epidemic models, providing criteria for selecting the appropriate model complexity for different populations and conditions, and analyzing when simpler models like the mass action SIR are valid.

Contribution

It introduces a hierarchy of epidemic models with conditions for substituting simpler models, and provides a rigorous framework for model selection based on population characteristics.

Findings

Conditions for using the mass action SIR model are established.

A procedure for selecting the appropriate epidemic model is proposed.

Rigorous convergence conditions for models to the mass action model are derived.

Abstract

We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the Mass Action model gives clear, rigorous conditions under which the Mass Action model is accurate.