On the Endemic Behavior of a Competitive Tri-Virus SIS Networked Model

TL;DR

This work identifies 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 coexisting equilibria.

Abstract

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.

Figures (1)

• Figure 1: Trajectories of the simulated trivirus system \ref{['eq:full']}, for different simulation parameters detailed in Section \ref{['sec:simulations']}.

Theorems & Definitions (9)

• Lemma 1
• Proposition 1
• Proposition 2
• Proposition 3
• Theorem 1
• Theorem 2
• Theorem 3
• Remark 1
• Theorem 4