Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview

TL;DR

This paper introduces edge-based compartmental modeling as a more realistic alternative to traditional models for infectious disease spread, accounting for social heterogeneity and contact duration.

Contribution

It derives simple ODE models incorporating contact heterogeneity and contact duration, and provides a graphical interpretation for easier understanding and application.

Findings

Models capture social heterogeneity in contact rates.

Explicitly considers contact duration effects.

Provides a graphical interpretation for model derivation.

Abstract

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes all individuals have the same contact rate and contacts are fleeting. This paper is the first of three investigating edge-based compartmental modeling, a technique eliminating these assumptions. In this paper, we derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of contact duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model. This paper focuses on the technique and how to apply it in different contexts. The companion papers investigate choosing the appropriate level of complexity for a model and how to apply edge-based compartmental modeling to populations with various sub-structures.