Towards Understanding the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model
This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. Specifically, the paper deals with three competing virus systems (i.e., tri-virus systems). First, we show that a tri-virus system, unlike a bi-virus system, is not a monotone dynamical system. Using the Parametric Transversality Theorem, we show that, generically, a tri-virus system has a finite number of equilibria and that the Jacobian matrices associated with each equilibrium are nonsingular. The endemic equilibria of this system can be classified as follows: a) single-virus endemic equilibria (also referred to as the boundary equilibria), where precisely one of the three viruses is alive; b) 2-coexistence equilibria, where exactly two of the three viruses are alive; and c) 3-coexistence equilibria, where all three viruses survive in the network. We provide a necessary and sufficient condition that guarantees local exponential convergence to a boundary equilibrium. Further, we secure conditions for the nonexistence of 3-coexistence equilibria (resp. for various forms of 2-coexistence equilibria). We also identify sufficient conditions for the existence of a 2-coexistence (resp. 3-coexistence) equilibrium. We identify conditions on the model parameters that give rise to a continuum of coexistence equilibria. More specifically, we establish i) a scenario that admits the existence and local exponential attractivity of a line of coexistence equilibria; and ii) scenarios that admit the existence of, and, in the case of one such scenario, global convergence to, a plane of 3-coexistence equilibria..
| Medienart: |
|
|---|
Preprint| Erscheinungsjahr: |
2023 |
|---|---|
| Erschienen: |
2023 |
| Enthalten in: |
arXiv.org - (2023) vom: 29. März Zur Gesamtaufnahme - year:2023 |
|---|
| Sprache: |
Englisch |
|---|
| Beteiligte Personen: |
Gracy, Sebin [VerfasserIn] |
|---|
| Links: |
Volltext [kostenfrei] |
|---|
| Themen: |
000 |
|---|
| Förderinstitution / Projekttitel: |
|
|---|
| PPN (Katalog-ID): |
XAR039107264 |
|---|
| LEADER | 01000naa a22002652 4500 | ||
|---|---|---|---|
| 001 | XAR039107264 | ||
| 003 | DE-627 | ||
| 005 | 20230330180142.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 230330s2023 xx |||||o 00| ||eng c | ||
| 035 | |a (DE-627)XAR039107264 | ||
| 035 | |a (arXiv)2303.16457 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 100 | 1 | |a Gracy, Sebin |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Towards Understanding the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model |
| 264 | 1 | |c 2023 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 520 | |a This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. Specifically, the paper deals with three competing virus systems (i.e., tri-virus systems). First, we show that a tri-virus system, unlike a bi-virus system, is not a monotone dynamical system. Using the Parametric Transversality Theorem, we show that, generically, a tri-virus system has a finite number of equilibria and that the Jacobian matrices associated with each equilibrium are nonsingular. The endemic equilibria of this system can be classified as follows: a) single-virus endemic equilibria (also referred to as the boundary equilibria), where precisely one of the three viruses is alive; b) 2-coexistence equilibria, where exactly two of the three viruses are alive; and c) 3-coexistence equilibria, where all three viruses survive in the network. We provide a necessary and sufficient condition that guarantees local exponential convergence to a boundary equilibrium. Further, we secure conditions for the nonexistence of 3-coexistence equilibria (resp. for various forms of 2-coexistence equilibria). We also identify sufficient conditions for the existence of a 2-coexistence (resp. 3-coexistence) equilibrium. We identify conditions on the model parameters that give rise to a continuum of coexistence equilibria. More specifically, we establish i) a scenario that admits the existence and local exponential attractivity of a line of coexistence equilibria; and ii) scenarios that admit the existence of, and, in the case of one such scenario, global convergence to, a plane of 3-coexistence equilibria. | ||
| 650 | 4 | |a Electrical Engineering and Systems Science - Systems and Control |7 (dpeaa)DE-84 | |
| 650 | 4 | |a Computer Science - Systems and Control |7 (dpeaa)DE-84 | |
| 650 | 4 | |a 620 |7 (dpeaa)DE-84 | |
| 650 | 4 | |a 000 |7 (dpeaa)DE-84 | |
| 700 | 1 | |a Ye, Mengbin |4 aut | |
| 700 | 1 | |a Anderson, Brian D. O. |4 aut | |
| 700 | 1 | |a Uribe, Cesar A. |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t arXiv.org |g (2023) vom: 29. März |
| 773 | 1 | 8 | |g year:2023 |g day:29 |g month:03 |
| 856 | 4 | 0 | |u https://arxiv.org/abs/2303.16457 |z kostenfrei |3 Volltext |
| 912 | |a GBV_XAR | ||
| 951 | |a AR | ||
| 952 | |j 2023 |b 29 |c 03 | ||