Theoretical epidemic simulations over varying tracing efforts and network overlap.

<p>(a) The maximum number of infected individuals (representing the peak of the epidemic), (b) its time of occurrence, and (c)-(d) the overall number of infected individuals on log and non-log scales, respectively; all plotted as a function of , with and . The legend shows the range of contact tracing effort, with to . We can see in (a) that contact tracing is effective in reducing the peak number of infected people with to times fewer maximum infected cases between and . We plot a line at , representing a minimal network overlap which corresponds to the values suggested by the analysis of mobile phone data (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0095133#pone-0095133-g004" target="_blank">figure 4</a>). The greater the overlap between the tracing and disease spreading networks, the more effective the tracing. At the ideal but unrealistic case of 100% overlap, a of 2.5 allows to get times fewer maximum infected people in comparison to the case with . A low overlap such as has little effect on the size of the outbreak (the overall number of infected individuals does not decrease much), but still the peak number of infected cases is lowered. With higher overlap, the peak of infections not only decreases in intensity but also gets delayed (c).