Before revision:  To tackle this, we approximate the susceptible-infected-susceptible (SIS) model on networks by a Birth-Death process , whose rates encode the structure of the underlying network and disease dynamics.
After revision:  To tackle this, epidemics on networks are approximated by a Birth-and-Death process which keeps track of the number of infected nodes at population level. The rates of this surrogate model encode both the structure of the underlying network and disease dynamics.