A Systematic Framework of Modelling Epidemics on Temporal Networks

TL;DR

This paper introduces a systematic modeling framework for epidemic spread on temporal networks, improving accuracy over existing models by shifting from edge-centric to pair-based descriptions, and analytically deriving epidemic thresholds.

Contribution

It presents a novel temporal pair-based epidemic model that enhances accuracy and provides analytical conditions for epidemic outbreaks on dynamic networks.

Findings

The pair-based model outperforms individual-based models in accuracy.

Exact modeling of Markovian epidemics on tree networks is achieved.

Epidemic thresholds are analytically derived from the model.

Abstract

We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from this framework offers an improvement over existing pair-based models by moving away from edge-centric descriptions while keeping the description concise and relatively simple. For the contagion process, we consider the Susceptible-Infected-Recovered (SIR) model, which is realized on a network with time-varying edges. We show that the shift in perspective from individual-based to pair-based quantities enables exact modelling of Markovian epidemic processes on temporal tree networks. On arbitrary networks, the proposed pair-based model provides a substantial increase in accuracy at a low computational and conceptual cost compared to the individual-based model. From the pair-based model, we analytically find the condition necessary for an epidemic to occur, otherwise known as the epidemic threshold. Due to the fact that the SIR model has only one stable fixed point, which is the global non-infected state, we identify an epidemic by looking at the initial stability of the model.