Stability properties of infected networks with low curing rates

Ali Khanafer, Tamer Başar, Bahman Gharesifard

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

Abstract

In this work, we analyze the stability properties of a recently proposed dynamical system that describes the evolution of the probability of infection in a network. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. When the curing rates at the nodes are low, a residual infection stays within the network. Using properties of Hurwitz Mertzel matrices, we show that the residual epidemic state is locally exponentially stable. We also demonstrate that this state is globally asymptotically stable. Furthermore, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. Several simulations demonstrate our results.

Original languageEnglish (US)
Title of host publication2014 American Control Conference, ACC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3579-3584
Number of pages6
ISBN (Print)9781479932726
DOIs
StatePublished - Jan 1 2014
Event2014 American Control Conference, ACC 2014 - Portland, OR, United States
Duration: Jun 4 2014Jun 6 2014

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2014 American Control Conference, ACC 2014
CountryUnited States
CityPortland, OR
Period6/4/146/6/14

Keywords

  • Constrained control
  • Networked control systems
  • Stability of nonlinear systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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  • Cite this

    Khanafer, A., Başar, T., & Gharesifard, B. (2014). Stability properties of infected networks with low curing rates. In 2014 American Control Conference, ACC 2014 (pp. 3579-3584). [6859418] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2014.6859418