Table 1.

Model inputs, parameters and prior distributions for Bayesian analysis.

Symbol	Definition (units)	Calibrated parameter(s)	Prior [Truncation]	Notes
N	Population size	Input (not calibrated)	Constant	40
Ninit	Initial IU on 2020–02-29	Ninit	LogN(1000, 10) [1, 10000]	¶
1/γ	Self-isolation time after contact tracing	Tisolation = 1/γ	LogN(14, 2) [7, 21]	ϯ
1/κ	Latent period (d)	Tlatent = 1/κ	N(4,1) [2,7]	41,42
c0	Baseline contact rate (contacts d−1)	c0	N(13, 5) [7, 20]	43
ρ	Recovery rate (d−1)	Trecover= 1/ρ	LogN(10, 1.5) [5, 30]	42,44
β0	Transmission probability per contact (unitless)	R0 = c0β0/ρ	N(2.9, 0.78) [1.46, 4.5]	45–47
fC	Fraction of contacts traced (unitless)	fC	LogN(0.25, 2) [0.05, 1]	48
fA	Fraction of infected asymptomatic (unitless)	fA	N(0.295,0.275) [0.02, 0.57]	49
T50T	Date of 50% of final testing rate (d)	T50T	U(60, 106) (Mar 1 – Apr 15)	¶
λ	General positive diagnosis rate (d−1)	λ = Ftest Senstest ktest	Derived	45,50,51
Ftest	General test coverage (unitless)	Ftest	Beta(2,2)	45,50,51
Senstest	Test sensitivity (unitless)	Senstest	N(0.7, 0.1) [0.6, 0.95]	52
ktest	General testing rate (d−1)	τtest = 1/ktest	N(7, 3) [2, 12]	53,54
λC	Contacts positive diagnosis rate (d−1)	λC = Senstest ktest,C	Derived
kC,test	Contacts testing rate (d−1)	τC,test = 1/kC,test	N(2, 1) [1, 3]	¶
ρC	Rate of infected contacts testing negative (d−1)	ρC = (1 – Senstest) ktest,C	Derived
δ	Fatal illness rate (d−1)	IFR (infected fatality rate)*	LogN(0.01, 2) [0.001, 0.1]	44,55
θmin	Minimum of θ(t)	θmin	Validation: Beta(2,2) Calibration: State-specific	¶ ƣ
τθ	Weibull scale parameter	τθ	Validation: N(21, 7) [7, 35] Calibration: State-specific	¶ ƣ
nθ	Weibull shape parameter	nθ	Validation: LogN(6, 2) [1,11] Calibration: State-specific	¶ ƣ
η	Hygiene effectiveness relative to social distancing (unitless)	η	Beta(2,4)	¶
τs	Duration of shelter in place (d)	τs	Validation: N(45, 30) [21, 90] Calibration: State-specific	56
τr	Duration of linear increase after shelter-in-place (d)	τr	Validation: N(45, 30) [14, 105] Calibration: State-specific	¶ ƣ
rmax	Maximum relative increase in contacts from shelter-in-place (unitless)	rmax	Validation: N(1, 1) [0, 2] Calibration: State-specific	¶ ƣ
τcase	Lag time for observing confirmed case	τcase	LogN(7, 2) [1, 14]	¶
τdeath	Lag time for observing confirmed death	τdeath	LogN(7, 2) [1, 14]	¶
αpos	Negative Binomial shape parameter for cases likelihood function	αpos	LogU(0.1, 40)	¶
αdeath	Negative Binomial shape parameter for deaths likelihood function	αdeath	LogU(0.1, 40)	¶

LogN(GM, GSD) = lognormal distribution with geometric mean GM and geometric standard deviation GSD

N(M,SD) = normal distribution with mean M and standard deviation SD

U(MIN,MAX) = uniform distribution with minimum MIN and maximum MAX

LogU(MIN, MAX) = log-uniform distribution with minimum MIN and maximum MAX

Beta(a,b) = beta distribution with shape parameters a and b

Time (t) is measured from t=1 corresponds to 2020–01-01.

^¶Assumed, non-informative prior wide enough to have adequate validation coverage.

^ϯStandard contact tracing guidance is to self-isolate for 2 weeks.

^ƣFor calibration to 6/20/20, state-specific priors were derived by fitting to different social distancing data sets, with each parameter’s mean, standard deviation, and range used to define a normal distribution prior.

^*See Methods for relationship between IFR and δ.