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/ɣ | Self-isolation time after contact tracing | Tisolation = 1/ɣ | 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.
Standard contact tracing guidance is to self-isolate for 2 weeks.
For 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.