Competitive Epidemic Spreading Over Networks

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 continuous-time 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.