Convergence and equilibria analysis of a networked bivirus epidemic model
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...
| Main Authors: | , , |
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| Format: | Journal Article |
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2022
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| Online Access: | http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/89027 |
| _version_ | 1848765142133637120 |
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| author | Ye, Mengbin Anderson, B.D.O. Liu, J.I. |
| author_facet | Ye, Mengbin Anderson, B.D.O. Liu, J.I. |
| author_sort | Ye, Mengbin |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T11:30:33Z |
| format | Journal Article |
| id | curtin-20.500.11937-89027 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:30:33Z |
| publishDate | 2022 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-890272022-09-06T09:10:18Z Convergence and equilibria analysis of a networked bivirus epidemic model Ye, Mengbin Anderson, B.D.O. Liu, J.I. 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. 2022 Journal Article http://hdl.handle.net/20.500.11937/89027 10.1137/20M1369014 http://purl.org/au-research/grants/arc/DP160104500 http://purl.org/au-research/grants/arc/DP190100887 fulltext |
| spellingShingle | Ye, Mengbin Anderson, B.D.O. Liu, J.I. Convergence and equilibria analysis of a networked bivirus epidemic model |
| title | Convergence and equilibria analysis of a networked bivirus epidemic model |
| title_full | Convergence and equilibria analysis of a networked bivirus epidemic model |
| title_fullStr | Convergence and equilibria analysis of a networked bivirus epidemic model |
| title_full_unstemmed | Convergence and equilibria analysis of a networked bivirus epidemic model |
| title_short | Convergence and equilibria analysis of a networked bivirus epidemic model |
| title_sort | convergence and equilibria analysis of a networked bivirus epidemic model |
| url | http://purl.org/au-research/grants/arc/DP160104500 http://purl.org/au-research/grants/arc/DP160104500 http://hdl.handle.net/20.500.11937/89027 |