Figure 2.

The graphs show stochastic iterations (blue) and four deterministic models carried out on the same computer-generated network: the full pair-wise model (Eq. 6) (red) and the approximation (Eq. 8) (cyan), as well as a mean-field model (Eq. 2) (black) and a k-regular pair-wise model (green) where all individuals are assumed to have the same, mean, number of neighbors k. (a) Typical time series with infection parameter τ/g = 0.35. (b) Equilibrium levels of infection over a range of the parameter τ/g including the mean and 90% confidence intervals from 200 stochastic iterations. (c) The basic reproductive ratio, R₀, over a range of the parameter τ/g; also included is the analytic value for an SIR type infection (mauve); the difference between the SIS and SIR approaches is evident. The stochastic R₀ is estimated by using the distribution of infection when the epidemic has reached the (low) level of infection at which, in the full model, growth rate hits its early-stage equilibrium. (d) The equilibrium distribution of infected individuals throughout the population compared with the distribution of all individuals, for τ/g = 0.27; more highly connected nodes, representing increasingly promiscuous individuals, are at a greater risk of infection.