Stability properties of infection diffusion dynamics over directed networks

Ali Khanafer; Tamer Basar; Bahman Gharesifard

doi:10.1109/CDC.2014.7040363

Stability properties of infection diffusion dynamics over directed networks

Ali Khanafer, Tamer Basar, Bahman Gharesifard

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We analyze the stability properties of a susceptible-infected-susceptible diffusion model over directed networks. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the all-healthy state is globally asymptotically stable (GAS). Otherwise, an endemic state arises and the entire network could become infected. Using notions from positive systems theory, we prove that the endemic state is GAS in strongly connected networks. When the graph is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of weak and strong endemic states. Several simulations demonstrate our results.

Original language	English (US)
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6215-6220
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7040363
State	Published - 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	12/15/14 → 12/17/14

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC.2014.7040363

Library availability

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Khanafer, A., Basar, T., & Gharesifard, B. (2014). Stability properties of infection diffusion dynamics over directed networks. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 6215-6220). Article 7040363 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7040363

Stability properties of infection diffusion dynamics over directed networks. / Khanafer, Ali; Basar, Tamer; Gharesifard, Bahman.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 6215-6220 7040363 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Khanafer, A, Basar, T & Gharesifard, B 2014, Stability properties of infection diffusion dynamics over directed networks. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7040363, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 6215-6220, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 12/15/14. https://doi.org/10.1109/CDC.2014.7040363

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Stability properties of infection diffusion dynamics over directed networks

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