Page 108 - Timeliness of Infectious Disease Notification & Response Systems - Corien Swaan

106 Chapter 4
Technical appendix
Mathematical Framework
Fraser et al. (6) introduced a framework to evaluate how controllable any infec- tious disease outbreak by calculating the proportion of new infections caused by an index until symptom onset, and subsequently evaluating outbreak control conditions by assuming that public health control measures take place imme- diately. Inspired by this idea, we propose a framework to evaluate timeliness by calculating the proportion of new infections caused by an infector until the moment the index case is reported to a PHA. By assuming that control measures take place at that moment, the proportion of potentially prevented cases can be assessed and outbreak control conditions can be evaluated. To set the layout of our framework we define the following:
· R, reproduction number: expected number of new infected cases genera- ted directly by one infector during his entire infectious period.
· τ, infection-age of an individual: time elapsed since the moment he/she is infected.
· g, Generation interval distribution: probability distribution of time interval between infection of an index case and infection of a secondary case.
· θ(τ), expected proportion of infections produced until infection-age τ. Par-
ticularly and most important in the present study, we denote:
◦ θr1 (PIR1 in the main manuscript), the expected proportion (or number if multiplied by R) of infections produced by an index case until he/she is re-
ported to the regional PHA.
◦ θr2 (PIR2 in the main manuscript), the expected proportion (or number if
multiplied by R) of infections produced by secondary cases until the index
case who produced them is reported to the regional PHA.
· finc(τ), incubation period distribution: probability distribution of time bet-
ween infection and symptom onset.
· N1(τ), reporting delay distribution: distribution of time between onset of
symptoms and reporting to PHA.