Table 3.

Mathematical transmission models fitted to data

First author	Publication date	Model*	Stochastic	Data†	Explicit SSEs	Mixing	Other key assumptions	Fitting methods	Results
Razum91	May 17, 2003	Exponential	No	HK 21/2–5/4	No	Homogeneous	··	LS to cumulative case numbers	Explains why models should not be fitted to cumulative case numbers
Riley92	June 20, 2003	SEIHR/D	Yes	HK 26/2–30/4	Yes	Metapopulation (homogeneous within districts)	Interventions reduced both community and hospital transmission; infectiousness reduced by 80% after hospital admission; used realistic incubation distributions.	ML to incidence; used waiting times estimated from individual case reports.	R0 excluding SSEs=2·7 reduced to 0·14 by end of epidemic; SSE contribution of order 0·3.
Lipsitch93	June 20, 2003	SEIR	No	HK 15/2–28/4; World 16/11–20/5	No	Homogeneous epidemic was	Assumed the case, matched growing exponentially (ie, there were no reductions in transmission caused by interventions).	For a given first model to final cumulative case numbers; serial interval estimated from Singapore outbreak.	R0=2·2–3·6
		Branching process	Yes	HK 15/2–19/4	No	Homogeneous	Assumed that there were no reductions in transmission caused by interventions.	Bayesian estimation with negative binomial distribution of secondary infections and Weibull distribution of serial intervals, both fitted to Singapore data.	R0 posterior mode=2·2, 95% credible interval 1·5–7·7
Galvani94	Aug 8, 2003	Exponential	No	All WHO data 18/3–11/5	No	Homogeneous	··	LS to cumulative case numbers.	Find a negative correlation between doubling time and CFR.
Chowell95	Sept 7, 2003	SEIHR	No	World, HK, Canada, Ontario 31/3–14/4	No	Homogeneous	Assumed the epidemic was growing exponentially.	LS to cumulative case numbers; most parameters fixed to plausible values.	R0=1·1–1·2
Ng96	Sept 10, 2003	SEIR	No	HK 17/3–12/5; Beijing, Inner Mongolia 21/4–12/5	No	Homogeneous	Assumed epidemic of unknown virus providing widespread protection to SARS resulted in decline in cases.	LS to cumulative case numbers.	Did not calculate R0; found that the model had difficulty explaining rapid decline of case numbers.
Choi53	Oct 1, 2003	SIHR/D	No	Canada 25/2–26/5	No	Homogeneous	Assumed discrete generations, with a fixed infectious/ incubating period of 5 days and time to death or recovery of 14 days; assumed no hospital transmission.	Fitted by trial and error to cumulative case and death reports.	R0=1·5, CFR=30%
Wang97	Nov 6, 2003	SEQIR	No	Beijing 27/4–2/6	No	Homogenous	Distinguish between suspected and probable cases.	Fit empirical time- dependent rates in simplified model to incidence.	R0=1·1–3·3
Zhou98	Dec 12, 2003	Curve fit	No	Beijing 21/4–24/6; HK 17/3–23/6; Singapore 17/3–30/5	No	Homogenous	··	LS to cumulative case numbers; fit an empirical curve.	R0=2·7 (Beijing), 2·1 (HK), 3·8 (Singapore), using method based on initial growth rate.93
Wallinga99	Sept 15, 2004	Branching process	Yes	HK, Vietnam, Singapore, Canada	No	No assumptions	Assume homogenous infectiousness	ML of who- infected-whom matrix and serial interval based on Singapore data	Detailed Rt curves, around 3 excluding SSEs, with large reduction to 0·7 after March 12.

^*In their simplest form, such model structures divide individuals into three compartments: susceptible (S), infected (I), and recovered (R), with recovered individuals assumed to be immune to further infection; for this reason, such models are often called SIR models. Extensions of SIR models have included additional classes of individuals: exposed (E, also known as latent), hospitalised (H), quarantined (Q), and dead (D).

^†Region and dates from which data were obtained for analysis. CFR=case fatality rate; HK=Hong Kong; LS=least squares; ML=maximum likelihood; SSE=super-spreading event; ··=not applicable.