Page 95 - Timeliness of Infectious Disease Notification & Response Systems - Corien Swaan

Quantifying reporting timeliness to improve outbreak control 93
tions expected by the index is 1, the light grey area under the curve. B) How the gene- ration interval distribution is modified, assuming that all index cases are notified and stopped exactly 13 days after exposure to the pathogen. C) How the average generation interval is modified when index cases are notified and stopped according to a time dis- tribution. Dark grey shading indicates the PIR1 value for each situation. The black line indicates the proportion of index cases not yet notified (right y-axis), equivalent to the probability of an index not yet being notified in each situation. PIR 1, expected propor- tion of cases caused by index case at notification.
Such a rapid response is not realistic, but the estimate provides an upper limit for outbreak control potential as determined by reporting speed. The calcula- tions were performed using scripts written in Python programming language (http: www.python.org). Below is an introductory explanation of our calculati- ons, for further details and explicit formulas are provided in the online Technical Appendix (http://wwwnc.cdc.gov/EID/article/21/2/13-0504-Tehcnapp1.pdf).
Calculation of PIR1, a 1-Generation-based Response
The generation interval is the time elapsed from the moment an infector acqui- res a pathogen until he/she infects another host. The distribution of the gene- ration interval time then indicates the average infective profile as time passes since an index acquired the pathogen (7). Figure 2, panel A, shows distribution of an index case generation interval: initially a period when no infections take place (latent period); then as time passes, the profile rises (beginning of infec- tious period) to a peak (most infections occur at this moment) and later decli- nes, leading to the end of the infectious period. We considered the reporting time elapsed since infection (RTSI) to be the addition of the symptom onset time (DINC) and the reporting delay (DOR) (Figure 1). Figure 2, panel B, shows PIR1 in the extreme case that RTSI is fixed at 13 days for every infector, meaning that the probability of not being reported before RTSI is 1, and after RTSI is 0.
The proportion of expected infections produced by an index case (PIR1) un- til reporting time is then provided by the area under the generation interval cur- ve weighted by the probability of not yet being reported, equivalent to the per- centage of nonreported cases. However, time for symptom onset and reporting delays vary from person to person and RTSI then becomes a distribution. This distribution smooths out the step-like probability of any infector not being re- ported at a given time (Figure 2, panel C), which consequently smooths out how the generation interval must be weighted for an appropriate PIR1 calculation.
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