Subgraph density and epidemics over networks

We model a SIS (susceptible-infected-susceptible) epidemics over a static, finite-sized network as a continuous-time Markov process using the scaled SIS epidemics model. In our previous work, we derived the closed form description of the equilibrium distribution that explicitly accounts for the network topology and showed that the most probable equilibrium state demonstrates threshold behavior. In this paper, we will show how subgraph structures in the network topology impact the most probable state of the long run behavior of a SIS epidemics (i.e., stochastic diffusion process) over any static, finite-sized, network.