Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Convergence and equilibria analysis of a networked bivirus epidemic model

    88851.pdf (711.8Kb)
    Access Status
    Open access
    Authors
    Ye, Mengbin
    Anderson, B.D.O.
    Liu, J.I.
    Date
    2022
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Mengbin, Y.E. and Anderson, B.D.O. and Liu, J.I. 2022. Convergence and equilibria analysis of a networked bivirus epidemic model. SIAM Journal on Control and Optimization. 60 (2): pp. S323-S346.
    Source Title
    SIAM Journal on Control and Optimization
    DOI
    10.1137/20M1369014
    ISSN
    0363-0129
    Funding and Sponsorship
    http://purl.org/au-research/grants/arc/DP160104500
    http://purl.org/au-research/grants/arc/DP190100887
    URI
    http://hdl.handle.net/20.500.11937/89027
    Collection
    • Curtin Research Publications
    Abstract

    This paper studies a networked bivirus model, in which two competing viruses spread across a network of interconnected populations; each node represents a population with a large number of individuals. The viruses may spread through possibly different network structures, and an individual cannot be simultaneously infected with both viruses. Focusing on convergence and equilibria analysis, a number of new results are provided. First, we show that for networks with generic system parameters, there exist a finite number of equilibria. Exploiting monotone systems theory, we further prove that for bivirus networks with generic system parameters, convergence to an equilibrium occurs for all initial conditions, except possibly for a set of measure zero. Given the network structure of one virus, a method is presented to construct an infinite family of network structures for the other virus that results in an infinite number of equilibria in which both viruses coexist. Necessary and sufficient conditions are derived for the local stability/instability of boundary equilibria, in which one virus is present and the other is extinct. A sufficient condition for a boundary equilibrium to be almost globally stable is presented. Then, we show how to use monotone systems theory to generate conclusions on the ordering of stable and unstable equilibria, and in some instances identify the number of equilibria via rapid simulation testing. Last, we provide an analytical method for computing equilibria in networks with only two nodes, and show that it is possible for a bivirus network to have an unstable coexistence equilibrium and two locally stable boundary equilibria.

    Related items

    Showing items related by title, author, creator and subject.

    • Competitive epidemic spreading over networks
      Ye, Mengbin ; Anderson, B.D.O. (2022)
      In this letter, we consider an epidemic model for two competitive viruses spreading over a metapopulation network, termed the ‘bivirus model’ for convenience. The dynamics are described by a networked continuoustime dynamical ...
    • Identifying DOS attacks using data pattern analysis
      Salem, Mohammed; Armstrong, Helen (2008)
      During a denial of service attack, it is difficult for a firewall to differentiate legitimate packets from rogue packets, particularly in large networks carrying substantial levels of traffic. Large networks commonly use ...
    • Taking a systems approach to explore the impacts and outcomes of a research and evaluation capacity building partnership: A protocol
      Tobin, Rochelle ; Hallett, Jonathan ; Lobo, Roanna ; Maycock, Bruce (2019)
      Introduction Partnership models that bring researchers, policymakers and service providers closer together are gaining traction as a strategy to improve public health practice. Yet, there is little evidence of how these ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.