Table 1 The intermediate variables of the model and their meaning
From: Impact of the Euro 2020 championship on the spread of COVID-19
Variable | Meaning | Equation |
|---|---|---|
\({R}_{{{{{{{{\rm{eff}}}}}}}},g,{g}^{{\prime} }}(t)\) | Effective reproduction number between genders g and \({g}^{{\prime} }\) | (4) |
Sg(t) | Number of susceptible persons of gender g | (2) |
Ig(t) | Number of infected persons of gender g | (1) |
N | Population size | |
G(τ) | Generation interval (Gamma kernel) | (3) |
Rbase(t) | Base reproduction number | (22) |
\(\Delta\)Rfootball(t) | Time dependent additive reproduction number due to football matches | (11) |
\(\Delta\)Rnoise(t) | Time dependent additive reproduction number due other non-balanced transmission | (31) |
\(\Delta\)Rmatch,m | Additive reproduction number of match m | (13) |
Cbase | Base contact matrix between genders | (5) |
Cmatch | Contact matrix for football related gatherings | (8) |
Cnoise | Contact matrix for other non-balanced transmission | (10) |
tm | Day of match m | |
αprior | Vector encoding country participation in matches | |
βprior | Vector encoding whether country hosted matches | |
\(\Delta\)αm | Difference of the effect of individual matches m (the country participated in) to mean effect of such matches | (15) |
\(\Delta\)βm | Difference of the effect of individual matches m (the country hosted) to mean effect of such matches | (20) |
γn(t) | Time-dependent base reproduction number in log-space between change point n and n + 1 | (24) |
\(\Delta\)γn | Effect of the change point n | (25) |
\({\tilde{\gamma }}_{n}(t)\) | Additive reproduction number due other non-balanced transmission between change point n and n + 1 | (33) |
\(\Delta {\tilde{\gamma }}_{n}\) | Effect of the change point n on the non-balanced transmission | (34) |
\({C}_{g}^{{{{\dagger}}} }(t)\) | Delayed number of infected persons of gender g | (40) |
\({\bar{D}}_{{{{{{{{\rm{country}}}}}}}}}\) | Country dependent reporting delay | Table 4 |
\({\hat{C}}_{g}(t)\) | Modeled number of cases of gender g | (44) |
ηt | Fraction of daily delayed cases | (45) |
rd | Average value of the fraction of delayed cases on weekday d | (46) |
\({r}_{d}^{{{{\dagger}}} }\) | Logit-transformed average value of the fraction of delayed cases on weekday d | (47) |
\(\Delta\)rd† | Deviation from the prior value of the fraction of delayed cases on weekday d | (50) |
Cg(t) | Measured number of cases of gender g | (53) |
\({R}_{{{{{{{{\rm{pre}}}}}}}}}\) | Reproduction number two weeks prior to the start of the Euro 2020 | Used in Fig. 3 |
Iprimary | Number of primary infected persons due to football matches | (65) |
Isubsequent | Number of subsequent infected persons due to football matches | (67) |
Inone | Number of infected persons without considering football matches | (67) |
