The Effectiveness of Contact Tracing in Emerging Epidemics

Klinkenberg, Don; Fraser, Christophe; Heesterbeek, Hans

The contour plots show that for some combinations of latent period and delay, the sensitivity to small changes in the delay is large (contours lie close to one another). Then, small changes in the delay can have a major impact when the time of quarantine is shifted from just before to just after the end of the latent period, similar to the sensitivity to t lat as observed in Figure 2 . This effect is most dramatic if there is little variation in the detection time (smallpox: d<0.7, and FMD: d<0.2). Figure 4 shows the effectiveness of single-step tracing for SARS, smallpox, influenza, and FMD using the parameter values listed in Figure 2 . The effectiveness of single-step contact tracing without tracing delays. Effectiveness is expressed as the minimum proportion of contacts that need to be traced for effective control (critical tracing probability p c *). The plots show p c * as a function of the latent period relative to the mean time to detection (t lat ). There are four special cases: A. Short infectious period and variable time to detection; B. Short infectious period and fixed detection time; C. Long infectious period and variable time to detection; and D. Long infectious period and fixed detection time. The three curves denote p c * for different values of the pre-isolation reproduction ratio R 0 pre . Indicated by dashed lines are the average t lat for four infections, in the panels with closest correspondence to the actual parameter values ( Table 2 ). Influenza appears in two panels with long and short infectious period, because it corresponds to both parameter sets equally. doi:10.1371/journal.pone.0000012.g002 Figure 3 . The effectiveness of single-step contact tracing with tracing delays, with the pre-detection reproduction ratio R 0 pre = 1.5. Effectiveness is expressed as the minimum proportion of contacts that need to be traced for effective control (critical tracing probability p c *). The contour plots show p c * as a function of the tracing delay d and the latent period t lat , measured relative to the mean detection time, for four special cases: A. Short infectious period and variable incubation period; B. Short infectious period and fixed incubation period; C. Long infectious period and variable incubation period; and D. Long infectious period and fixed incubation period. Dark grey shadows indicate areas where tracing is ineffective, light grey shadows indicate areas where p c * = 0.33. Indicated by dashed lines are the average t lat for four infections, in the panels with closest correspondence to the actual parameter values ( Table 2 ). Influenza appears in two panels with long and short infectious period, because it corresponds to both parameter sets equally. doi:10.1371/journal.pone.0000012.g003 Figure 4 . The effectiveness of single-step and iterative contact tracing for control of influenza, smallpox, SARS, and foot-and-mouth disease. Effectiveness is expressed as the minimum proportion of contacts that need to be traced for effective control (critical tracing probability p c *); p c * is plotted as a function of the relative delay (d, proportion of the incubation period) or the absolute delay (days). doi:10.1371/journal.pone.0000012.g004 Table 2 . Panel 4A shows the relation between p c * and the relative tracing delay d, from which it appears that the general cases shown in Figures 2 and 3 are good predictors for assessing tracing effectiveness. Influenza can be placed somewhere between long and short infecti