Page 109 - Timeliness of Infectious Disease Notification & Response Systems - Corien Swaan

Quantifying reporting timeliness to improve outbreak control 107
One-generation based response. We assumed transmission from the reported case is instantaneously stopped from the moment of reporting. We calculated θr1 (PIR1 in the main document) by integrating the effective first generation in- terval g1e(τ)=g(τ)(1-[N1*finc](τ)) in τ (Fig. 2C in the main document). As defined above, g(τ) is the conventional generation interval distribution, finc(τ) the incu- bation period distribution and N1(τ) the reporting delay distribution.
The convolution
[N1*finc](τ) =oN1(t)finc(τ-t)dt
represents the probability of an index being reported at infection-age τ.
Two-generation based response (contact tracing). We considered the hypothe- tical intervention where contacts (secondary cases) are traced and stopped (to- gether with their source person) instantly from transmitting onwards at notifi- cation time of the index case. We calculated θr2 (PIR2 in the main manuscript) by integration in τ of the effective second generation interval g2e(τ)=g2(τ)(1-[N1*finc] (τ)) (Fig. 3B.in the main document), with [N1*finc](τ) as defined above. Here g2(τ) is the generation interval distribution of secondary cases as function of infec- tion-age of their index case and is computed by the convolution [g*g1e](τ)= og(t) g1e(τ-t)dt , where g1e(τ) is the effective first generation interval defined above.
Influence of reporting delay spread (standard deviation) on expected proportion of infections
We calculated θr1 and θr2 values (PIR1 and PIR2 in the main document, respec- tively) using various reporting delay distributions. This allowed us to study how much reporting delay variations influence the values of θr1 and θr2.
To cover a range of various reporting delay distributions we parametrised in terms of median and standard deviation (SD) and used a set of these pa- rameters. Notification median delays ranged from 1 to 60 days, in steps of 1 day. Standard deviations were chosen as multiples 0, 0.5, 1, 1.5 and 2 of the median. The Appendix Figure shows that the expected proportion of infections caused by index (θr1, or PIR1) and by secondary cases (θr2, or PIR2) are highly dependent on reporting delay medians. However, the figure also shows that θr1 and θr2 do not sensitively depend on standard deviation values within the range matching actual reporting delay distributions (SD=0.5-1.5*median, see Table 1 in the main document).
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