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

We study 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., tri-virus system). First, we show that the tri-virus system is not monotone. Thereafter, we identify necessary conditions and a sufficient condition for local exponential convergence to a boundary equilibrium (exactly one virus is alive, and the other two are dead) and identify a special case that admits the existence and local exponential attractivity of a line of coexisting 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 coexisting equilibria.