Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms

Abstract

Given a contact network that changes over time (say, day vs night connectivity), and the SIS (susceptible/infected/susceptible, flu like) virus propagation model, what can we say about its epidemic threshold? That is, can we determine when a small infection will "take-off" and create an epidemic? Consequently then, which nodes should we immunize to prevent an epidemic? This is a very real problem, since, e.g. people have different connections during the day at work, and during the night at home. Static graphs have been studied for a long time, with numerous analytical results. Time-evolving networks are so hard to analyze, that most existing works are simulation studies [5]. Specifically, our contributions in this paper are: (a) we formulate the problem by approximating it by a Non-linear Dynamical system (NLDS), (b) we derive the first closed formula for the epidemic threshold of timevarying graphs under the SIS model, and finally (c) we show the usefulness of our threshold by presenting efficient heuristics and evaluate the effectiveness of our methods on synthetic and real data like the MIT reality mining graphs.

Epidemic Spread in Mobile Ad Hoc Networks: Determining the Tipping Point

“…If the mobility model can be represented as a sequence of graphs, then the epidemic threshold depends on the first eigenvalue of the system matrix [25].…”

Control Strategies of Contagion Processes in Time-Varying Networks

“…A closed formula for the epidemic threshold of a SIS epidemic process unfolding on any time-varying has been derived [77]. In this approach the time-varying network is considered as a sequence of adjacency matrices A 1 , A 2 , .…”

“…In their work, Prakash et al [77] used their analytical derivation of the epidemic threshold in a general time-varying network mentioned above, to study the efficiency of different controlling strategies in a real network obtained from the MIT Reality Mining project [84]. This dataset describes the interactions of 104 students recorded via Bluetooth.…”

Understanding and managing cascades on large graphs

“…al. gave the epidemic threshold for arbitrarily varying dynamic networks [24,27]. We will also cover recent work on understanding models involving competition between multiple contagions ('iPhone vs Android') [20,21,22,3].…”

“…In this part, the aim is to leverage and utilize the understanding gained in Part 1, to actually manage such processes for our benefit -like algorithms for finding best people to immunize [5,26,24], finding the best people to market Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.…”