Stability properties of infection diffusion dynamics over directed networks

Ali Khanafer, Tamer Basar, Bahman Gharesifard

Research output: Contribution to journalConference article

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 languageEnglish (US)
Article number7040363
Pages (from-to)6215-6220
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume2015-February
Issue numberFebruary
DOIs
StatePublished - Jan 1 2014
Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
Duration: Dec 15 2014Dec 17 2014

Fingerprint

Directed Network
System theory
Asymptotic stability
Infection
Curing
Dynamic models
Globally Asymptotically Stable
Threshold Phenomena
Positive Systems
Global Asymptotic Stability
Diffusion Model
Systems Theory
Existence and Uniqueness
Entire
Graph in graph theory
Demonstrate
Simulation
Model

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Stability properties of infection diffusion dynamics over directed networks. / Khanafer, Ali; Basar, Tamer; Gharesifard, Bahman.

In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7040363, 01.01.2014, p. 6215-6220.

Research output: Contribution to journalConference article

Khanafer, Ali ; Basar, Tamer ; Gharesifard, Bahman. / Stability properties of infection diffusion dynamics over directed networks. In: Proceedings of the IEEE Conference on Decision and Control. 2014 ; Vol. 2015-February, No. February. pp. 6215-6220.
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