Improved bounds on the epidemic threshold of exact SIS models on complex networks

Navid Azizan Ruhi, Christos Thrampoulidis, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations


The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a 2n-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and, in particular, determining the threshold of epidemic spread quite challenging. It has been shown that the exact marginal probabilities of infection can be upper bounded by an n-dimensional linear time-invariant system, a consequence of which is that the Markov chain is “fast-mixing” when the LTI system is stable, i.e. when equation (where β is the infection rate per link, δ is the recovery rate, and λmax(A) is the largest eigenvalue of the network's adjacency matrix). This well-known threshold has been recently shown not to be tight in several cases, such as in a star network. In this paper, we provide tighter upper bounds on the exact marginal probabilities of infection, by also taking pairwise infection probabilities into account. Based on this improved bound, we derive tighter eigenvalue conditions that guarantee fast mixing (i.e., logarithmic mixing time) of the chain. We demonstrate the improvement of the threshold condition by comparing the new bound with the known one on various networks with various epidemic parameters.
Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control (CDC)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages6
ISBN (Print)9781509018376
StatePublished - Jan 5 2017
Externally publishedYes


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