When Is a Network Epidemic Hard to Eliminate?
Author(s)
Drakopoulos, Kimon; Koksal, Asuman E.; Tsitsiklis, John N
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We consider the propagation of a contagion process (“epidemic”) on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. For bounded degree graphs, we provide a lower bound on the expected time to extinction under any such dynamic allocation policy, in terms of a combinatorial quantity that we call the resistance of the set of initially infected nodes, the available budget, and the number of nodes n.
Specifically, we consider the case of bounded degree graphs, with the resistance growing linearly in n. We show that if the curing budget is less than a certain multiple of the resistance, then the expected time to extinction grows exponentially with n. As a corollary, if all nodes are initially infected and the CutWidth of the graph grows linearly, while the curing budget is less than a certain multiple of the CutWidth, then the expected time to extinction grows exponentially in n. The combination of the latter with our prior work establishes a fairly sharp phase transition on the expected time to extinction (sublinear versus exponential) based on the relation between the CutWidth and the curing budget.
Date issued
2016-09Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision SystemsJournal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Drakopoulos, Kimon et al. “When Is a Network Epidemic Hard to Eliminate?” Mathematics of Operations Research 42, 1 (January 2017): 1–14 © 2017 Institute for Operations Research and the Management Sciences (INFORMS)
Version: Original manuscript
ISSN
0364-765X
1526-5471