Epidemic Threshold of an SIS Model in Dynamic Switching Networks

TL;DR

This paper derives an epidemic threshold for SIS models in dynamic switching networks, using joint spectral radius, and validates it across various network types, including static, periodic, and regular networks.

Contribution

It introduces a novel epidemic threshold based on joint spectral radius for dynamic networks, extending classical results to time-varying topologies.

Findings

Epidemic threshold derived for dynamic switching networks.

Threshold matches classical results for static networks.

Upper bound for epidemic spread in Gilbert networks.

Abstract

In this paper, we analyze dynamic switching networks, wherein the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold, considering the SIS epidemic model. First, an epidemic probabilistic model is developed assuming independence between states of nodes. We identify the conditions under which the epidemic dies out by linearizing the underlying dynamical system and analyzing its asymptotic stability around the origin. The concept of joint spectral radius is then used to derive the epidemic threshold, which is later validated using several networks (Watts-Strogatz, Barabasi-Albert, MIT reality mining graphs, Regular, and Gilbert). A simplified version of the epidemic threshold is proposed for undirected networks. Moreover, in the case of static networks, the derived epidemic threshold is shown to match conventional analytical results. Then, analytical results for the epidemic threshold of dynamic networksare proved to be applicable to periodic networks. For dynamic regular networks, we demonstrate that the epidemic threshold is identical to the epidemic threshold for static regular networks. An upper bound for the epidemic spread probability in dynamic Gilbert networks is also derived and verified using simulation.