Multi-competitive viruses over time-varying networks with mutations and human awareness

In this paper, we introduce a model for multiple competing viruses over networks, derived using each state variable of the model as the infection percentage of a group or a subpopulation. We show that the model is well-posed, and also compare it to a full probabilistic Markov model. We provide a necessary and sufficient condition for uniqueness of the healthy state (the origin) of the multi-virus model over static graphs. We also provide several sufficient conditions for convergence to the healthy state for mutating viruses over dynamic networks. We analyze various endemic states of the multi-virus model over static graphs, including providing necessary and sufficient conditions for the existence of parallel equilibria. We further extend the model to include an awareness state, allowing nodes to become alerted to the fact that viruses are spreading in the system and therefore reduce their susceptibility, and analyze the equilibria of such a model. Finally, we propose several antidote control techniques and present a set of illustrative simulations.