(a) Estimation of τ/g by using the prevalence of infection on a network taken from Wylie and Jolly (11), for chlamydia and gonorrhea and three different models: the full pair-wise, the mean-field, and the k-regular. (b) For the same network, evaluation of the effectiveness of control strategies by using the pair-wise network model. The equilibrium infection prevalence is shown as the two control methods are varied. One is the infection parameter τ/g relative to the estimated value; this is a measure of the change in infectivity attributable to random screening or public awareness. The other is the contact tracing efficiency, the proportion of infected partners who are successfully traced and treated once an index case is identified. The dashed red line shows the corresponding extinction threshold for the mean-field model, which is unaffected by contact tracing.