NDLI: SIRS epidemics on complex networks: Concurrence of exact Markov chain and approximated models

Content Provider	IEEE Xplore Digital Library
Author	Ruhi, Navid Azizan Hassibi, Babak
Copyright Year	2015
Description	Author affiliation: California Institute of Technology, Pasadena, 91125, USA (Ruhi, Navid Azizan; Hassibi, Babak)
Abstract	We study the SIRS (Susceptible-Infected-Recovered-Susceptible) spreading processes over complex networks, by considering its exact 3n-state Markov chain model. The Markov chain model exhibits an interesting connection with its 2n-state nonlinear “mean-field” approximation and the latter's corresponding linear approximation. We show that under the specific threshold where the disease-free state is a globally stable fixed point of both the linear and nonlinear models, the exact underlying Markov chain has an O(log n) mixing time, which means the epidemic dies out quickly. In fact, the epidemic eradication condition coincides for all the three models. Furthermore, when the threshold condition is violated, which indicates that the linear model is not stable, we show that there exists a unique second fixed point for the nonlinear model, which corresponds to the endemic state. We also investigate the effect of adding immunization to the SIRS epidemics by introducing two different models, depending on the efficacy of the vaccine. Our results indicate that immunization improves the threshold of epidemic eradication. Furthermore, the common threshold for fast-mixing of the Markov chain and global stability of the disease-free fixed point improves by the same factor for the vaccination-dominant model.
Starting Page	2919
Ending Page	2926
File Size	381364
Page Count	8
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7402660
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Markov processes Mathematical model Eigenvalues and eigenfunctions Stability analysis Yttrium Nickel Complex networks
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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