Table 2.

Infection characteristics estimated by the TSIR model. The approximate generation time of each infection determines the discrete time step used in the TSIR model

Infection	TSIR time step		Mean reporting proportion	Mean βs	R2
Measles	Biweekly	0·2207	0·004 (0·002)	5·41 (1·52)	0·92
		(95% CI 0·2197–0·2217)
Mumps	Monthly	0·1277	0·034 (0·007)	10·53 (0·78)	0·98
		(95% CI 0·1274–0·1281)
Rubella	Biweekly	0·2807	0·017 (0·002)	4·72 (0·18)	0·99
		(95% CI 0·2788–0·2825)
Varicella	Biweekly	0·80	0·092 (0·02)	1·79 (0·06)	0·93
		(95% CI 0·7996–0·8)
Scarlet fever	Biweekly	0·80	0·006 (0·001)	1·75 (0·06)	0·91
		(95% CI 0·8–0·8)
Pertussis	Monthly	0·0533	0·001 (0·0001)	24·65 (5·21)	0·93
		(95% CI 0·0531–0·0533)

TSIR, Time-series susceptible-infected-recovered; CI, confidence interval.

is the estimated mean proportion of susceptibles in the population (95% CIs in parentheses, derived from the profile likelihood using the χ² distribution with 1 degree of freedom). Mean reporting proportion is the mean of the time-varying reported rates estimated using locally varying regression of cumulative births on cumulative cases (standard deviation of the time-varying rates in parentheses). Mean β_s is the mean value of the seasonal transmission rates estimated via the TSIR model (maximum standard error in parentheses). The R² values (on a log scale) for the TSIR fit are measured as 1 – [residual deviance/null deviance].