Epidemic Threshold of an SIS Model in Dynamic Switching Networks

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 susceptible-infected-susceptible epidemic model. First, an epidemic probabilistic model is dev...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2016-03, Vol.46 (3), p.345-355
Main Authors: Sanatkar, Mohammad Reza, White, Warren N., Natarajan, Balasubramaniam, Scoglio, Caterina M., Garrett, Karen A.
Format: Article
Language:English
Subjects:
Asymptotic stability
Dynamic networks
Dynamic tests
dynamical system
Dynamical systems
Dynamics
epidemic threshold
Epidemics
Indexes
Joints
Mathematical analysis
Mathematical model
Network topology
Networks
Switches
Switching theory
Symmetric matrices
Thresholds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 susceptible-infected-susceptible 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 networks are 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.
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2015.2448061