Complex equilibria patterns in weakly-coupled competitive bivirus epidemic networks

In this paper, we study an epidemic spreading process using a bivirus Susceptible-Infected-Susceptible (SIS) network model, which examines two competing viruses spreading through a network of populations. We consider the scenario where two separate bivirus networks are weakly coupled to form a single system. We derive analytical results on how the equilibria pattern of the joined system, in particular the number of equilibria and their stability properties, is determined by the equilibria patterns of the two separate systems. In particular, we account for every possible pairing of one equilibrium from each of the two separate systems, and provide conditions governing when one can associate this pair with an equilibrium of the joined system, as well as the associated stability characteristics. A numerical example illustrates the complex patterns that can emerge from weak coupling of two bivirus networks.