Introduction
Methods
Model structure
Description | Baseline value | Refs. |
---|---|---|
Average time a person remains in the non-infectious latency state (\(\alpha\)) | \(lognormal(7,3)^{b}\) | [25] |
Proportion of asymtomatic people (f) | 0.40 | [26] |
Average recovery time (\(\gamma _1\)) | 15 days | [27] |
Proportion of hospitalized people (\(\sigma _1\)) | 0.23 | |
Median number of days from symptom onset to hospitalization (\(\gamma _2\)) | 4 (1, 9) days | [30] |
Median number of days of hospitalization (\(\gamma _3\)) | 6 (3, 10) days | [30] |
Percent that die among those hospitalized (\(\sigma _2\)) | 11.8% | [31] |
Shedding probability | 0.38 | [a] |
Infection probability | 0.38 | [a] |
Introduction probability | 0.05 | [a] |
Assumptions for the scenarios | ||
Percentage of staff using PPE | 90% | [a] |
Percentage of residents using PPE | 75% | [a] |
PPE effect (\(OR_{pi}\)) | 0.1467 | [a] [32] |
Detection probability | \(80\%\) | [a] |
Percentage of staff tested | \(90\%\) | [a] |
Percentage of resident tested | \(33.3\%\) | [a] |
Frequency of testing | Weekly | [a] |
Vaccine effect (\(OR_{\upsilon }\)) | 0.0493 | [a] [33] |
Vaccine immunity duration | 120 days | [a] |
Distribution of the staff agent characteristics | ||
CN contacts per hour | \(Multinom \sim (X_{0}=0.7,X_1=0.3)\) | |
RN contacts per hour | \(Multinom \sim (X_0 = 0.25, X_1 =0.75)\) | |
LPN contacts per hour | \(Multinom \sim (X_0=0.15,X_2=0.2,X_3=0.25, X_4 =0.2, X_5 =0.2)\) | |
Work schedule | \(Multinom \sim (X_{morning}=0.4, X_{afternoon}=0.4, X_{night}=0.2)\) | |
Staff type | \(Multinom \sim (X_{CN}=0.6, X_{RN}=0.15, X_{LPN}=0.15)\) |
Disease dynamics
Staff and resident interactions
COVID-19 transmission in the community
Interventions
Model implementation
Analysis of outcomes and sensitivity analysis
Parameter name | Definition | Sample space |
---|---|---|
Infection_p | Global transmission probability | (0.304, 0.38, 0.456) |
Introduction_p | Probability of introduction from the community | (0.01, 0.05, 0.1) |
AsymptTransmission | Asymptomatic transmission | (0.34, 0.42, 0.99) [39] |
SR_OR | Reduction on transmission when comparing staff to residents | (0.5, 0.7, 1.0) |
TestingFreq | Frequency of testing (days) | (3, 5, 7) |
detection_p | Probability of correctly identifying a COVID-19 positive case | (0.64, 0.8, 0.96) |
PPE_OR | Influence of PPE in reduction of transmission expressed as odds ratios | (0.0722, 0.1467, 0.3408) [32] |
VaccineEff | Vaccine efficacy | (Equal, A, B) |
vaccination_dist | Distribution of the vaccine amongst residents and staff | (0.0, 0.3, 0.5, 0.7) |
Results
Baseline scenario
Parameter | Days to eradication | Attack rate | Total infected | Infected residents | Infected staff | Hospitalizations | Deaths |
---|---|---|---|---|---|---|---|
Baseline | 106.46 (99.9, 112.88) | 0.29 (0.26, 0.31) | 98.5 (90, 106) | 60 (54.5, 65) | 38 (35, 41) | 25.5 (23, 27.5) | 3 (2.5, 3.5) |
Transmission probability | |||||||
Low transmission (0.304) | \(-\) 19.96(\(-\) 26.68,\(-\) 13.24)* | \(-\) 0.12(\(-\) 0.16,\(-\) 0.09)* | \(-\) 42.73(\(-\) 53.82,\(-\) 31.65)* | \(-\) 26.06(\(-\) 32.8,\(-\) 19.31)* | \(-\) 16.68(\(-\) 21.12,\(-\) 12.23)* | \(-\) 10.79(\(-\) 13.68,\(-\) 7.9)* | \(-\) 1.38(\(-\) 1.79,\(-\) 0.97)* |
High transmission (0.42) | 9.81(2.95,16.68)* | 0.11(0.07,0.14)* | 36.4(25.08,47.71)* | 21.83(14.94,28.71)* | 14.57(10.03,19.11)* | 9.27(6.32,12.22)* | 1.13(0.72,1.55)* |
Introduction probability | |||||||
Low introduction probability (0.01) | \(-\) 26.82(\(-\) 33.71,\(-\)19.93)* | 0(\(-\) 0.04,0.03)* | \(-\) 0.28(\(-\) 12.44,11.89)* | \(-\) 3.34(\(-\) 10.66,3.99)* | 3.06(\(-\) 1.85,7.97)* | \(-\) 1.56(\(-\) 4.69,1.57)* | \(-\) 0.22(\(-\) 0.65,0.22)* |
High introduction probability (0.1) | 3.38(\(-\) 3.7,10.47)* | 0.11(0.07,0.14)* | 37.29(24.78,49.81)* | 26.52(18.98,34.06)* | 10.78(5.72,15.83)* | 11.28(8.06,14.5)* | 1.41(0.96,1.86)* |
Detection probability | |||||||
Low detection probability (0.64) | 10.16(1.68,18.64)* | 0.03(\(-\) 0.01,0.07)* | 10.81(\(-\) 3.15,24.78)* | 7.9(\(-\) 0.54,16.34)* | 2.92(\(-\) 2.75,8.58)* | 3.54(\(-\) 0.09,7.17)* | 0.3(\(-\) 0.23,0.82)* |
High detection probability (0.9) | \(-\) 23.49(\(-\) 30.17,\(-\) 16.82)* | \(-\) 0.19(\(-\) 0.22,\(-\) 0.16)* | \(-\) 65.23(\(-\) 76.23,\(-\) 54.23)* | \(-\) 40.11(\(-\) 46.76,\(-\) 33.47)* | \(-\) 25.12(\(-\) 29.58,\(-\) 20.66)* | \(-\) 16.49(\(-\) 19.35,\(-\) 13.63)* | \(-\) 1.86(\(-\) 2.27,\(-\) 1.45)* |
PPE effect | |||||||
High effect PPE (0.07) | \(-\) 41.73(\(-\) 52.31,\(-\) 31.14)* | \(-\) 0.09(\(-\) 0.13,\(-\) 0.04)* | \(-\) 29.24(\(-\) 46.43,\(-\) 12.05)* | \(-\) 17.58(\(-\) 27.98,\(-\) 7.17)* | \(-\) 11.66(\(-\) 18.63,\(-\) 4.7)* | \(-\) 7.14(\(-\) 11.62,\(-\) 2.66)* | \(-\) 1.03(\(-\) 1.68,\(-\) 0.37)* |
Low effect PPE (0.34) | 22.13(16.63,27.63)* | 0.22(0.19,0.24)* | 75.13(66.2,84.06)* | 46.32(40.91,51.72)* | 28.82(25.2,32.43)* | 19.35(17.02,21.68)* | 2.21(1.87,2.55)* |
Asymptomatic transmission | |||||||
Low asymptomatic transmission (0.34) | 21.44(12.12,30.76)* | 0.08(0.04,0.13)* | 29.14(13.41,44.86)* | 18.27(8.75,27.79)* | 10.86(4.52,17.21)* | 7.7(3.63,11.77)* | 0.89(0.31,1.47)* |
High asymptomatic transmission (0.99) | 26.85(18.19,35.52)* | 0.23(0.19,0.27)* | 78.69(64.06,93.32)* | 49.4(40.54,58.26)* | 29.29(23.39,35.19)* | 21.18(17.4,24.96)* | 2.24(1.7,2.77)* |
Age specific difference in transmission | |||||||
High age specific difference (0.34) | \(-\) 2.11(\(-\)9.08,4.86) | 0(\(-\) 0.04,0.03) | \(-\) 0.33(\(-\)12.47,11.8) | 0.25(\(-\) 7.12,7.63) | \(-\) 0.59(\(-\)5.44,4.26) | 0.14(\(-\) 3.01,3.29) | 0(\(-\) 0.44,0.44) |
Low age specific difference (0.99) | \(-\) 4.64(\(-\) 11.56,2.28) | 0(\(-\) 0.04,0.03) | \(-\) 0.8(\(-\) 12.86,11.25) | \(-\) 0.77(\(-\) 8.1,6.56) | \(-\) 0.04(\(-\) 4.86,4.79) | \(-\) 0.13(\(-\) 3.26,3) | 0.01(\(-\) 0.43,0.44) |
Testing frequency | |||||||
Testing frequency, 5-daysa | \(-\) 26.98(\(-\) 36.51,\(-\) 17.44)* | \(-\) 0.12(\(-\) 0.14,\(-\) 0.1)* | \(-\) 41.68(\(-\) 49.52,\(-\) 33.84)* | \(-\) 24.85(\(-\) 29.75,\(-\) 19.95)* | \(-\) 16.83(\(-\) 19.89,\(-\) 13.77)* | \(-\) 9.94(\(-\) 12.16,\(-\) 7.72)* | \(-\) 1.18(\(-\) 1.55,\(-\) 0.82)* |
Testing frequency, 3-daysa | \(-\) 48.53(\(-\) 58.31,\(-\) 38.76)* | \(-\) 0.17(\(-\) 0.19,\(-\) 0.14)* | \(-\) 57.33(\(-\) 65.37,\(-\) 49.29)* | \(-\) 34.57(\(-\) 39.59,\(-\) 29.55)* | \(-\) 22.76(\(-\) 25.9,\(-\) 19.62)* | \(-\) 14.59(\(-\) 16.86,\(-\) 12.31)* | \(-\) 1.71(\(-\) 2.08,\(-\) 1.34)* |
Vaccine distribution (when compared to no vaccination) | |||||||
Equal distribution | \(-\) 38.89(\(-\) 42.38,\(-\) 35.4)* | \(-\) 0.16(\(-\) 0.17,\(-\) 0.14)* | \(-\) 53.66(\(-\) 58.48,\(-\) 48.85)* | \(-\) 33.29(\(-\) 36.21,\(-\) 30.36)* | \(-\) 20.37(\(-\) 22.34,\(-\) 18.41)* | \(-\) 13.76(\(-\) 15.01,\(-\) 12.5)* | \(-\) 1.65(\(-\) 1.82,\(-\) 1.47)* |
Resident priority | \(-\) 34.08(\(-\) 37.67,\(-\) 30.48)* | \(-\) 0.15(\(-\) 0.17,\(-\) 0.14)* | \(-\) 52.95(\(-\) 57.92,\(-\) 47.98)* | \(-\) 36.16(\(-\) 39.18,\(-\) 33.14)* | \(-\) 16.79(\(-\) 18.82,\(-\) 14.76)* | \(-\) 15.05(\(-\) 16.34,\(-\) 13.75)* | \(-\) 1.82(\(-\) 2,\(-\) 1.63)* |
Staff priority | \(-\) 42.09(\(-\) 45.62,\(-\) 38.55)* | \(-\) 0.16(\(-\) 0.18,\(-\) 0.15)* | \(-\) 56.14(\(-\) 61.02,\(-\) 51.27)* | \(-\) 32.45(\(-\) 35.41,\(-\) 29.48)* | \(-\) 23.7(\(-\) 25.69,\(-\) 21.71)* | \(-\) 13.66(\(-\) 14.93,\(-\) 12.39)* | \(-\) 1.7(\(-\) 1.88,\(-\) 1.52)* |
Vaccine effect (when compared to similar age-specific effect) | |||||||
Different age-specific vaccine efficacy [Pfizer] (0.06b,0.04c) | \(-\) 1.12(\(-\) 4.41,2.17) | 0(\(-\) 0.01,0.01) | \(-\) 0.98(\(-\) 4.1,2.13) | \(-\) 0.76(\(-\) 2.65,1.14) | \(-\) 0.23(\(-\) 1.59,1.14) | \(-\) 0.32(\(-\) 1.15,0.51) | \(-\) 0.07(\(-\) 0.19,0.06) |
Different age-specific vaccine efficacy [Moderna] (0.13b, 0.04c) | 3.7(0.36,7.03)* | 0.01(0,0.02)* | 3.93(0.78,7.09)* | 1.37(\(-\) 0.55,3.29) | 2.56(1.18,3.95)* | 0.58(\(-\) 0.26,1.43) | 0.05(\(-\) 0.08,0.17) |
Sensitivity analysis
Testing and vaccine interventions
Scenario | Days to eradication | Attack rate | Total Infected | Infected residents | Infected staff | Hospitalizations | Deaths |
---|---|---|---|---|---|---|---|
Introduction probability & testing frequencya | |||||||
High & 5-days | \(-\) 11.22(\(-\) 34.84,12.4)* | \(-\) 0.19(\(-\) 0.27,\(-\) 0.11)* | \(-\) 65.29(\(-\) 91.41,\(-\) 39.16)* | \(-\) 37.5(− 54.66,− 20.34)* | − 27.79(− 37.08,− 18.49)* | − 12.95(− 21.63,− 4.26)* | − 2.07(− 3.48,− 0.66)* |
High & 3-days | \(-\) 51.11(\(-\) 75.06,\(-\) 27.16)* | \(-\) 0.29(\(-\) 0.37,\(-\) 0.21)* | \(-\) 99.08(\(-\) 125.56,\(-\) 72.59)* | − 59.23(− 76.63,− 41.83)* | − 39.85(− 49.27,− 30.43)* | − 24.07(− 32.87,− 15.26)* | − 3.08(− 4.5,− 1.65)* |
Moderate & 5-days | \(-\) 26.06(\(-\) 36.14,\(-\) 15.98)* | \(-\) 0.12(\(-\) 0.14,\(-\) 0.1)* | \(-\) 41.19(\(-\) 49.4,\(-\) 32.97)* | − 24.86(− 30.02,− 19.71)* | − 16.32(− 19.51,− 13.14)* | − 10.16(− 12.49,− 7.82)* | − 1.19(− 1.57,− 0.8)* |
Moderate & 3-days | \(-\) 49.44(\(-\) 59.81,\(-\) 39.07)* | \(-\) 0.17(\(-\) 0.19,\(-\) 0.14)* | \(-\) 57.51(\(-\) 65.96,\(-\) 49.06)* | − 35.06(− 40.36,− 29.75)* | − 22.45(− 25.73,− 19.18)* | − 14.9(− 17.31,− 12.5)* | − 1.75(− 2.15,− 1.36)* |
Low & 5-days | \(-\) 38.54(\(-\) 65.84,\(-\) 11.23)* | \(-\) 0.16(\(-\) 0.24,\(-\) 0.07)* | \(-\) 53.36(\(-\) 83.49,\(-\) 23.23)* | − 29.8(− 46.98,− 12.62)* | − 23.56(− 36.66,− 10.46)* | − 13.76(− 21.93,− 5.58)* | − 1.31(− 2.48,− 0.15)* |
Low & 3-days | \(-\) 45.36(\(-\) 72.66,\(-\) 18.05)* | \(-\) 0.16(\(-\) 0.25,\(-\) 0.07)* | \(-\) 55.49(\(-\) 85.62,\(-\) 25.36)* | − 30.53(− 47.71,− 13.36)* | − 24.96(− 38.06,− 11.86)* | − 13.89(− 22.07,− 5.71)* | − 1.51(− 2.68,− 0.35)* |
Introduction probability & vaccine prioritization | |||||||
High & resident | 2.01(\(-\) 3.61,7.62) | \(-\) 0.01(\(-\) 0.03,0.01) | \(-\) 3.26(\(-\) 10.11,3.59) | \(-\) 6.79(\(-\) 11.16,\(-\) 2.43)* | 3.53(0.81,6.24)* | − 3.27(− 5.18,− 1.35)* | − 0.5(− 0.79,− 0.2)* |
High & staff | \(-\) 5.1(\(-\) 10.6, \(-\) 0.4)* | \(-\) 0.02(\(-\) 0.04,0) | \(-\) 6.18(\(-\) 12.89,0.52) | \(-\) 0.71(\(-\) 4.99,3.57)* | − 5.47(− 8.13,− 2.82)* | − 0.81(− 2.68,1.07)* | − 0.19(− 0.49,0.1)* |
Moderate & resident | 5.22(0.88,9.57)* | 0(\(-\) 0.01,0.01) | \(-\) 0.06(\(-\) 3.85,3.73) | \(-\) 2.58(\(-\) 4.87,\(-\) 0.3)* | 2.53(0.89,4.16)* | \(-\) 1.11(− 2.11,− 0.11)* | − 0.2(− 0.35,− 0.06)* |
Moderate & staff | \(-\) 2(\(-\) 6.89,2.9) | 0(\(-\) 0.02,0.01) | \(-\) 1.19(\(-\) 5.58,3.2) | 2.02(\(-\) 0.62,4.66) | \(-\) 3.21(\(-\) 5.12,− 1.31)* | 0.74(− 0.42,1.9) | − 0.05(− 0.22,0.12) |
Low & resident | 1.96(\(-\) 3.52,7.45) | 0.01(0,0.03)* | 3.97(\(-\) 0.8,8.75) | 0(\(-\) 2.45,2.45) | 3.98(1.49,6.46)* | 0(\(-\) 1.06,1.06) | 0.16(0,0.32) |
Low & staff | \(-\) 6.36(\(-\) 11.74,\(-\) 0.99)* | \(-\) 0.01(\(-\) 0.02,0)* | \(-\) 3.09(\(-\) 7.77,1.59) | \(-\) 1.05(\(-\) 3.45,1.35) | − 2.04(− 4.48,0.4) | − 0.72(− 1.77,0.32) | 0.01(− 0.15,0.16) |