Some elementary properties of SIR networks or, can i get sick because you got vaccinated?

We consider epidemics on social networks and address the question of whether administering a safe vaccine to one or more individuals can raise another individual's chances of becoming infected. Surprisingly, this can happen if transmission probabilities vary over time. If transmission probabilities do not vary with time, we show that in the discrete SIR model vaccination cannot cause collateral damage. We phrase this question in terms of monotonicity properties and answer it using bond percolation methods. By passing to a covering graph we are able to extend these results to models with more complicated latent and infective states.