Analysis and Control of a Continuous-Time Bi-Virus Model

Ji Liu, Philip E. Pare, Angelia Nedic, Choon Yik Tang, Carolyn L. Beck, Tamer Basar

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the equilibria of the system and their stability. Specifically, when the two viruses spread over possibly different directed infection graphs, the system may have the following: first, a unique equilibrium, the healthy state, which is globally stable, implying that both viruses will eventually be eradicated, second, two equilibria including the healthy state and a dominant virus state, which is almost globally stable, implying that one virus will pervade the entire network causing a single-virus epidemic while the other virus will be eradicated, or third, at least three equilibria including the healthy state and two dominant virus states, depending on certain conditions on the healing and infection rates. When the two viruses spread over the same directed infection graph, the system may have zero or infinitely many coexisting epidemic equilibria, which represents the pervasion of the two viruses. Sensitivity properties of some nontrivial equilibria are investigated in the context of a decentralized control technique, and an impossibility result is given for a certain type of distributed feedback controller.

Original languageEnglish (US)
Article number8638525
Pages (from-to)4891-4906
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 2019


  • Competing viruses
  • computer viruses
  • epidemic processes
  • networked control systems
  • nonlinear control systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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