Before considering these approaches on networks, it is worth considering what is meant by nonnetwork mixing and showing explicitly how this can derive the standard transmission terms from familiar differential equation models. Nonnetwork mixing can be taken to have one of two meanings: either that every individual in the population is weakly connected to every other (the mean-field assumption), or that an Erdös-Rényi random graph defines the transmission network, depending on context. To see how this determines the epidemic dynamics, we consider a population of N individuals, with a homogeneous independent probability q that any pair of individuals is linked on the network, which gives each individual a mean number of edges n = q(N − 1). We then assume that the transmission rate for infection across an edge is τ and that the proportion of the population infectious at a time t is I(t); then, the force of infection experienced by an average susceptible in the population is nτI(t) ≡ βI(t). The quantity β, therefore, defines a population-level transmission rate that can be interpreted in one of two ways as N → ∞. In the case where the population is assumed to be fully connected, the limit is that q is held at unity, and so τ is reduced to as N is increased to hold q(N − 1)τ constant. In the case where the population is connected on a random graph, q is reduced as N is increased to hold n constant.