Figure 1.
Single-step and iterative tracing on an epidemic tree, developing from left to right.
Nodes are infecteds, lines are contacts, contactees that were not infected are not represented on the tree. Grey infecteds are asymptomatic, white infecteds are symptomatic, infecteds with a thick border are isolated or quarantined.
Solid lines are traceable contacts, dotted lines are untraceable contacts.
A. Single-step tracing.
In A1a-c, a symptomatic infected is isolated and his traceable contactees are quarantined.
In A2a-b (some time later), one of the quarantined infecteds got symptomatic and his traceable contactees are quarantined.
B. Iterative tracing.
In B1a-c, a symptomatic infected is isolated and all infecteds directly or indirectly linked to this infected by traceable contacts are quarantined.
All quarantined infecteds form a traceable cluster.
Table 1.
List of most important parameters.
Table 2.
Parameter values for the real infections
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 pc *).
The plots show pc * as a function of the latent period relative to the mean time to detection (τlat).
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 pc * for different values of the pre-isolation reproduction ratio R 0 pre .
Indicated by dashed lines are the average τlat 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.
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 pc *).
The contour plots show pc * as a function of the tracing delay δ and the latent period τlat, 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 pc * = 0.33.
Indicated by dashed lines are the average τlat 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.
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 pc *); pc * is plotted as a function of the relative delay (δ, proportion of the incubation period) or the absolute delay (days).