  The paper deals with the analysis of a discrete-time networked competitive
bivirus susceptible-infected-susceptible (SIS) model. More specifically, we
suppose that virus 1 and virus 2 are circulating in the population and are in
competition with each other. We show that the model is strongly monotone, and
that, under certain assumptions, it does not admit any periodic orbit. We
identify a sufficient condition for exponential convergence to the disease-free
equilibrium (DFE). Assuming only virus 1 (resp. virus 2) is alive, we establish
a condition for global asymptotic convergence to the single-virus endemic
equilibrium of virus 1 (resp. virus 2) -- our proof does not rely on the
construction of a Lyapunov function. Assuming both virus 1 and virus 2 are
alive, we establish a condition which ensures local exponential convergence to
the single-virus equilibrium of virus 1 (resp. virus 2). Finally, we provide a
sufficient (resp. necessary) condition for the existence of a coexistence
equilibrium.
