Connecting Mass-action Models and Network Models for Infectious Diseases

TL;DR

This paper explores the relationship between mass-action and network models in infectious disease modeling, proposing methods to connect and compare their predictions, especially on arbitrary networks, with theoretical and empirical validation.

Contribution

It introduces a spreading rule linking fully connected network models to mass-action models and a method to map epidemic spread on arbitrary networks to mass-action-like models, with theoretical justification.

Findings

Identifies a spreading rule matching fully connected network and mass-action models.

Proposes a method to map epidemic spread on arbitrary networks to mass-action models.

Demonstrates advantages of the methods using synthetic data based on empirical networks.

Abstract

Infectious disease modeling is used to forecast epidemics and assess the effectiveness of intervention strategies. Although the core assumption of mass-action models of homogeneously mixed population is often implausible, they are nevertheless routinely used in studying epidemics and provide useful insights. Network models can account for the heterogeneous mixing of populations, which is especially important for studying sexually transmitted diseases. Despite the abundance of research on mass-action and network models, the relationship between them is not well understood. Here, we attempt to bridge the gap by first identifying a spreading rule that results in an exact match between disease spreading on a fully connected network and the classic mass-action models. We then propose a method for mapping epidemic spread on arbitrary networks to a form similar to that of mass-action models. We also provide a theoretical justification for the procedure. Finally, we show the advantages of the proposed methods using synthetic data that is based on an empirical network. These findings help us understand when mass-action models and network models are expected to provide similar results and identify reasons when they do not.