Universality of the SIS prevalence in networks

TL;DR

This paper introduces a universal spectral-based analytical curve that accurately bounds the prevalence of SIS epidemic processes across diverse network types and infection parameters, enhancing understanding of epidemic dynamics.

Contribution

It presents a novel spectral decomposition method that yields a universal, analytic curve applicable to various SIS and SIR models on different network structures, including temporal and disconnected graphs.

Findings

Universal curve bounds prevalence over time in SIS models.

Method applies to both homogeneous and heterogeneous infection rates.

Accuracy comparable to mean-field approximations.

Abstract

Epidemic models are increasingly used in real-world networks to understand diffusion phenomena (such as the spread of diseases, emotions, innovations, failures) or the transport of information (such as news, memes in social on-line networks). A new analysis of the prevalence, the expected number of infected nodes in a network, is presented and physically interpreted. The analysis method is based on spectral decomposition and leads to a universal, analytic curve, that can bound the time-varying prevalence in any finite time interval. Moreover, that universal curve also applies to various types of Susceptible-Infected-Susceptible (SIS) (and Susceptible-Infected-Removed (SIR)) infection processes, with both homogenous and heterogeneous infection characteristics (curing and infection rates), in temporal and even disconnected graphs and in SIS processes with and without self-infections. The accuracy of the universal curve is comparable to that of well-established mean-field approximations.