where Z n ∞ (τ, γ) is the expected final size of an epidemic in a household of size n with one initial infected. Of course, the within-and between-community mixing for real networks is likely to be much more complex than may be captured by a Poisson process, but these two extremes can provide useful insights. These models show that network structure of the form of communities reduces the potential for an infectious disease to spread, and hence, greater transmission rates are required for the disease to exceed the invasion threshold.