On the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909359241428992 |
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| author | Gracy, Sebin Ye, Mengbin Anderson, Brian DO Uribe, Cesar A. |
| author_facet | Gracy, Sebin Ye, Mengbin Anderson, Brian DO Uribe, Cesar A. |
| contents | This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. In particular, we focus on the case where there are three competing viruses (i.e., the tri-virus system). First, we show that the tri-virus system is not a monotone system. Thereafter, we provide a condition that guarantees local exponential convergence to a boundary equilibrium (exactly one virus is endemic, the other two are dead), and identify a special case that admits the existence and local exponential attractivity of a line of coexistence equilibria (at least two viruses are active). Finally, we identify a particular case (subsumed by the aforementioned special case) such that, for all nonzero initial infection levels, the dynamics of the tri-virus system converge to a plane of coexistence equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_11826 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model Gracy, Sebin Ye, Mengbin Anderson, Brian DO Uribe, Cesar A. Systems and Control This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. In particular, we focus on the case where there are three competing viruses (i.e., the tri-virus system). First, we show that the tri-virus system is not a monotone system. Thereafter, we provide a condition that guarantees local exponential convergence to a boundary equilibrium (exactly one virus is endemic, the other two are dead), and identify a special case that admits the existence and local exponential attractivity of a line of coexistence equilibria (at least two viruses are active). Finally, we identify a particular case (subsumed by the aforementioned special case) such that, for all nonzero initial infection levels, the dynamics of the tri-virus system converge to a plane of coexistence equilibria. |
| title | On the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2209.11826 |