Before revision:  We consider the presence of additive noise in a deterministic SIS model over a random graph sampled from a piecewise Lipschitz graphon with finite rank. We derive a noise index to evaluate the deviation from the disease-free state due to noise.
After revision:  We consider the presence of additive noise in a linearized SIS model and we derive a noise index to evaluate the deviation from the disease-free state due to noise.