Multi-competitive time-varying networked SIS model with an infrastructure network

The paper studies the problem of the spread of multi-competitive viruses across a (time-varying) population network and an infrastructure network. To this end, we devise a variant of the classic (networked) susceptible-infected-susceptible (SIS) model called the multi-competitive time-varying networked susceptible-infected-water-susceptible (SIWS) model. We establish a sufficient condition for exponentially fast eradication of a virus when a) the graph structure does not change over time; b) the graph structure possibly changes with time, interactions between individuals are symmetric, and all individuals have the same healing and infection rate; and c) the graph is directed and is slowly-varying, and not all individuals necessarily have the same healing and infection rates. We also show that the aforementioned conditions for eradication of a virus are robust to variations in the graph structure of the population network provided the variations are not too large. For the case of time-invariant graphs, we give a lower bound on the number of equilibria that our system possesses. Finally, we provide an in-depth set of simulations that not only illustrate the theoretical findings of this paper but also provide insights into the endemic behavior for the case of time-varying graphs.