  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.
