| Summary: | In this letter, we consider an epidemic model
for two competitive viruses spreading over a metapopulation
network, termed the ‘bivirus model’ for convenience.
The dynamics are described by a networked continuoustime
dynamical system, with each node representing a population
and edges representing infection pathways for the
viruses.We survey existing results on the bivirus model beginning
with the nature of the equilibria, including whether
they are isolated, and where they exist within the state
space with the corresponding interpretation in the context
of epidemics. We identify key convergence results, including
the conclusion that for generic system parameters,
global convergence occurs for almost all initial conditions.
Conditions relating to the stability properties of various
equilibria are also presented. In presenting these results,
we also recall some of the key tools and theories used to
secure them. We conclude by discussing the various open
problems, ranging from control and network optimization,
to further characterization of equilibria, and finally extensions
such as modeling three or more viruses.
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