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This study extends the SIS epidemic model for single virus propagation overan arbitrary graph to an SI1SI2S epidemic model of two exclusive, competitiveviruses over a two-layer network with generic structure, where network layersrepresent the distinct transmission routes of the viruses. We find analyticalresults determining extinction, mutual exclusion, and coexistence of theviruses by introducing the concepts of survival threshold and winningthreshold. Furthermore, we show the possibility of coexistence in SIS-typecompetitive spreading over multilayer networks. Not only do we rigorously provea region of coexistence, we quantitate it via interrelation of central nodesacross the network layers. Little to no overlapping of layers central nodes isthe key determinant of coexistence. Specifically, we show coexistence isimpossible if network layers are identical yet possible if the network layershave distinct dominant eigenvectors and node degree vectors. For example, weshow both analytically and numerically that positive correlation of networklayers makes it difficult for a virus to survive while in a network withnegatively correlated layers survival is easier but total removal of the othervirus is more difficult. We believe our methodology has great potentials forapplication to broader classes of multi-pathogen spreading over multi-layer andinterconnected networks.

May the Best Meme Win!: New Exploration of Competitive Epidemic Spreading over Arbitrary Multi-Layer Networks