Figures and data in The effect of variation of individual infectiousness on SARS-CoV-2 transmission in households

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Tables
Additional files

7 figures, 16 tables and 1 additional file

Figures

Figure 1

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Summary of statistics for 17 identified studies.

Figure shows the average number of contacts and standard deviation (SD) of number of contact, SD of number of secondary cases per index cases ( $σ_{s e c}$ ), and secondary attack rate (SAR) for 17 identified studies.

Figure 2

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Modeling results of household transmission dynamics and infectiousness variation.

Figure shows the estimates of infectiousness variation ( $σ_{v a r}$ ), the estimated probability of infection from community and estimated probability of infection from households, and the reduction in deviance information criteriion (DIC) compared with the model without infectiousness variation. Models are fitted separately to 14 household transmission studies.

Figure 3

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Estimate distribution of relative infectiousness based on the pooled estimate.

Red line indicates the estimated distribution and the gray lines indicate the associated uncertainty. Black dashed line indicates average infectiousness (relative infectiousness equal to 1), while the purple and blue dashed lines indicate top 20% and 10% infectiousness, respectively.

Figure 4

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Relationship between infectiousness variation and statistic.

In each panel, numbers represent the observed corresponding relationship for the identified studies. Panels A and B show the relationship between infectiousness variation ( $σ_{v a r}$ ) and secondary attack rate (SAR) and standard deviation (SD) of number of secondary cases per index cases ( $σ_{s e c}$ ). In the bottom, numbers in bracket indicate the number of household contacts in corresponding studies.

Appendix 1—figure 1

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Appendix 1—figure 2

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Correlation plots for the posterior distribution of model parameters in Lyngse et al., Carazo et al., Laxminarayan et al., and Dattner et al.

Appendix 1—figure 3

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The density plot of the distribution of infectiousness profile since infections, used in the modeling analysis.

Tables

Appendix 1—table 1

Summary of characteristic of identified studies.

Author (year)	Location	Study period	Case ascertainment method	Test coverage of identified contacts	SARS-COV-2 variant	Public health and social measures
Lyngse et al., 2022	Denmark	February 2020 to August 2020	Index: RT-PCR Secondary: RT-PCR	All contacts were tested	Ancestral strains	Lockdown
Carazo et al., 2022	Canada	March 2020 to June 2020	Index: RT-PCR Secondary: Symptom-based	NA	Ancestral strains	Handwashing, mask-wearing, and physical distancing
Laxminarayan et al., 2020	India	March 2020 to July 2020	Index: RT-PCR Secondary: RT-PCR	All contacts were tested	Ancestral strains	Lockdown, social distancing, contact tracing
Dattner et al., 2021	Israel	March 2020 to June 2020	Index: RT-PCR and Serology Secondary: RT-PCR and Serology	All contacts were tested	Ancestral strains	Lockdown
Layan et al., 2022	Israel	December 2020 to April 2021	Index: RT-PCR Secondary: RT-PCR	All contacts were tested	Ancestral strains, alpha	Vaccination
Hart et al., 2022	UK	March 2020 to November 2020	Index: RT-PCR Secondary: RT-PCR and antibody test	All contacts were tested	Ancestral strains	Isolation
Hubiche et al., 2021	Canada	April 2020 to June 2020	Index: Symptom-based and RT-PCR and serology Secondary: Symptom-based and RT-PCR and serology	NA	Ancestral strains	Closure of school
Wilkinson et al., 2021	Manitoba, Canada	Mid-January 2020 to late March 2020	Index: NAAT assay Secondary: NAAT assay	Only symptomatic contacts were tested	Ancestral strains	Isolation and contact tracing
Tsang et al., 2022	Shandong Province, China	January 2020 to May 2020	Index: RT-PCR Secondary: RT-PCR	All contacts were tested	Ancestral strains	Isolation, mask-waring, social distancing
Reukers et al., 2021	Netherlands	March 2020 to May 2020	Index: RT-PCR Secondary: RT-PCR	NA	Ancestral strains	Social distancing
Han et al., 2022	Netherlands	March 2020 to April 2020	Index: RT-PCR and serology Secondary: RT-PCR and serology	All contacts were tested	Ancestral strains	Social distancing, self-quarantine and self-isolation orders, closure of schools, bars and restaurants, and urging people to work from home
Méndez-Echevarría et al., 2021	Madrid, Spain	March 2020 to May 2020	Index: RT-PCR and serology Secondary: RT-PCR and serology	All contacts were tested	Ancestral strains	Lockdown
Dutta et al., 2020	Rajasthan, India	May 2020 to July 2020	Index: RT‐PCR Secondary: RT‐PCR	All contacts were tested	Ancestral strains	Lockdown and stay-at-home orders, physical distancing
Koureas et al., 2021	Greece	April 2020 to June 2020	Index: RT-PCR Secondary: RT-PCR	All contacts were tested	Ancestral strains	Quarantine, screening, movement restrictions and gathering prohibition, isolation
Bernardes-Souza et al., 2021; Méndez-Echevarría et al., 2021	Brazil	May 2020 to June 2020	Index: Serology and RT-PCR Secondary: Serology	All contacts were tested	Ancestral strains	Lockdown, gathering restrictions and face mask mandates
Posfay-Barbe et al., 2020	Switzerland	March 2020 to April 2020	Index: RT-PCR Secondary: RT-PCR	NA	Ancestral strains	Closure of schools, daycares, restaurants, bars, and shops, social distancing
Hsu et al., 2021	Taiwan, China	January 2020 to February 2021	Index: RT-PCR Secondary: RT-PCR	Only symptomatic contacts were tested	Ancestral strains, alpha	Mask-wearing, hand washing, and social distancing

Appendix 1—table 2

Summary of model estimates.

Article	Estimates of infectiousness variation	Estimates of probability of infection from community (10^–2)	Estimates of probability of infection from household	Relationship between transmission and number of contacts ( $β_{})$
Lyngse et al.	1.48 (1.29, 1.7)	0.06 (0, 0.16)	0.1 (0.08, 0.12)	0.72 (0.59, 0.89)
Carazo et al.	1.41 (1.19, 1.72)	0.2 (0.01, 0.43)	0.3 (0.24, 0.34)	0.75 (0.62, 0.93)
Laxminarayan et al.	2.44 (1.98, 3.23)	0.03 (0, 0.11)	0.04 (0.01, 0.07)	0.92 (0.69, 1)
Dattner et al.	1.12 (0.65, 1.69)	0.63 (0.12, 1.06)	0.31 (0.19, 0.42)	0.65 (0.45, 0.91)
Layan et al.	1.12 (0.74, 1.76)	0.3 (0.02, 0.96)	0.26 (0.15, 0.39)	0.2 (0.01, 0.6)
Hart et al.	0.35 (0.11, 0.96)	0.74 (0.05, 2.12)	0.51 (0.32, 0.65)	0.72 (0.32, 0.98)
Hubiche et al.	1.03 (0.45, 2.68)	1.24 (0.14, 2.48)	0.32 (0.06, 0.57)	0.67 (0.13, 0.98)
Wilkinson et al.	1.05 (0.12, 3.51)	0.32 (0.02, 0.91)	0.07 (0, 0.18)	0.43 (0.02, 0.97)
Tsang et al.	2.83 (1.48, 4.73)	0.45 (0.05, 1.03)	0.06 (0, 0.26)	0.66 (0.06, 0.99)
Reukers et al.	1.79 (0.72, 4.5)	1.53 (0.18, 2.93)	0.22 (0.01, 0.6)	0.67 (0.07, 0.98)
Han et al.	1.71 (0.51, 4.13)	1.67 (0.19, 2.99)	0.21 (0.02, 0.61)	0.69 (0.07, 0.99)
Méndez-Echevarría et al.	0.51 (0.13, 1.7)	0.91 (0.05, 2.53)	0.28 (0.06, 0.52)	0.57 (0.04, 0.98)
Dutta et al.	1.53 (0.5, 4.2)	1.1 (0.12, 2.26)	0.24 (0.01, 0.63)	0.78 (0.15, 0.99)
Koureas et al.	1.88 (0.6, 3.66)	0.84 (0.1, 1.76)	0.13 (0.01, 0.42)	0.44 (0.02, 0.96)

Appendix 1—table 3

Model adequacy check for Lyngse et al.

Each element of the table has the format observed frequency – expected (posterior mean) frequency (95% credible interval).

Number of household contacts	Number of infected household contacts
Number of household contacts	0	1	2	3	4	5
1	2366–2377 (2319, 2433)	569–558 (502, 616)	NA	NA	NA	NA
2	1117–1105 (1070, 1138)	227–227 (198, 259)	77–88 (69, 109)	NA	NA	NA
3	1135–1118 (1077, 1156)	214–235 (203, 267)	89–86 (67, 106)	41–41 (27, 56)	NA	NA
4	521–528 (501, 555)	119–115 (94, 137)	40–42 (30, 56)	25–19 (11, 30)	11–10 (4, 18)	NA
5	161–167 (152, 181)	42–38 (27, 50)	14–14 (7, 22)	7–7 (2, 12)	7–3 (0, 8)	0–2 (0, 5)

Appendix 1—table 4

Model adequacy check for Carazo et al.

Each element of the table has the format observed frequency – expected (posterior mean) frequency (95% credible interval).

Number of household contacts	Number of infected household contacts
Number of household contacts	0	1	2	3	4	5
1	803–814 (765, 862)	532–521 (473, 570)	NA	NA	NA	NA
2	476–454 (423, 485)	179–186 (160, 212)	154–169 (144, 195)	NA	NA	NA
3	518–520 (483, 557)	201–202 (175, 232)	132–130 (107, 155)	133–131 (106, 158)	NA	NA
4	217–221 (197, 245)	85–87 (70, 106)	52–52 (39, 67)	43–39 (27, 52)	45–41 (28, 56)	NA
5	76–74 (61, 88)	30–30 (20, 41)	20–18 (10, 26)	13–12 (6, 20)	7–10 (5, 17)	10–11 (5, 18)

Appendix 1—table 5

Model adequacy check for Laxminarayan et al.

Each element of the table has the format observed frequency – expected (posterior mean) frequency (95% credible interval).

Number of household contacts	Number of infected household contacts
Number of household contacts	0	1	2	3	4	5	6	7	8	9
1	124–134 (122, 144)	37–27 (17, 39)	NA	NA	NA	NA	NA	NA	NA	NA
2	135–137 (125, 147)	12–18 (10, 27)	20–12 (6, 20)	NA	NA	NA	NA	NA	NA	NA
3	188–176 (163, 188)	13–22 (13, 33)	11–9 (4, 16)	5–9 (4, 17)	NA	NA	NA	NA	NA	NA
4	127–118 (108, 128)	11–15 (8, 23)	5–5 (1, 11)	3–3 (0, 7)	1–4 (1, 10)	NA	NA	NA	NA	NA
5	75–76 (67, 84)	12–10 (4, 16)	3–3 (0, 8)	1–2 (0, 5)	1–1 (0, 4)	3–2 (0, 6)	NA	NA	NA	NA
6	41–40 (34, 46)	7–5 (1, 10)	2–2 (0, 5)	0–1 (0, 3)	0–0 (0, 3)	0–0 (0, 2)	1–1 (0, 3)	NA	NA	NA
7	32–31 (25, 36)	3–4 (1, 9)	2–1 (0, 4)	1–1 (0, 3)	1–0 (0, 2)	0–0 (0, 2)	0–0 (0, 2)	0–0 (0, 3)	NA	NA
8	10–13 (10, 16)	2–2 (0, 5)	3–0 (0, 2)	1–0 (0, 2)	0–0 (0, 1)	1–0 (0, 1)	0–0 (0, 1)	0–0 (0, 1)	0–0 (0, 1)	NA
9	14–16 (12, 20)	2–2 (0, 6)	1–1 (0, 3)	2–0 (0, 2)	1–0 (0, 2)	0–0 (0, 1)	0–0 (0, 1)	0–0 (0, 1)	0–0 (0, 1)	1–0 (0, 2)

Appendix 1—table 6

Model adequacy check for Dattner et al.

Each element of the table has the format observed frequency – expected (posterior mean) frequency (95% credible interval).

Number of household contacts	Number of infected household contacts
Number of household contacts	0	1	2	3	4	5	6	7	8	9
1	85–93 (77, 108)	73–65 (50, 81)	NA	NA	NA	NA	NA	NA	NA	NA
2	46–42 (32, 52)	21–25 (17, 34)	19–19 (11, 28)	NA	NA	NA	NA	NA	NA	NA
3	38–29 (21, 38)	13–18 (11, 25)	9–12 (6, 19)	8–9 (4, 15)	NA	NA	NA	NA	NA	NA
4	24–24 (16, 32)	19–15 (9, 23)	11–10 (5, 17)	8–7 (3, 13)	1–5 (1, 11)	NA	NA	NA	NA	NA
5	25–21 (14, 30)	15–15 (9, 22)	12–10 (5, 17)	7–7 (3, 13)	3–5 (2, 10)	2–4 (1, 9)	NA	NA	NA	NA
6	13–16 (9, 23)	19–12 (6, 18)	3–8 (3, 14)	5–6 (2, 11)	3–5 (1, 9)	5–3 (0, 7)	5–2 (0, 6)	NA	NA	NA
7	5–9 (4, 15)	6–7 (3, 13)	5–5 (2, 10)	7–4 (1, 8)	4–3 (0, 7)	4–2 (0, 6)	4–2 (0, 5)	0–1 (0, 4)	NA	NA
8	10–8 (3, 14)	7–7 (3, 12)	3–5 (1, 10)	4–4 (1, 8)	0–3 (0, 7)	3–2 (0, 6)	3–2 (0, 5)	4–1 (0, 4)	0–1 (0, 4)	NA
9	6–6 (2, 12)	3–6 (2, 10)	4–4 (1, 9)	6–3 (0, 7)	4–3 (0, 6)	1–2 (0, 5)	2–2 (0, 5)	2–1 (0, 4)	2–1 (0, 3)	0–0 (0, 3)

Appendix 1—table 7

Comparison of model estimates from 100k Markov chain Monte Carlo (MCMC) iterations and 500k MCMC iterations.

Article	Number of MCMC iterations	Estimates of infectiousness variation	Estimates of probability of infection from community (10^–2)	Estimates of probability of infection from household	Relationship between transmission and number of contacts ( $β)$
Lyngse et al.	100,000	1.48 (1.29, 1.7)	0.06 (0, 0.16)	0.11 (0.08, 0.13)	0.72 (0.59, 0.89)
	500,000	1.49 (1.29, 1.84)	0.07 (0, 0.2)	0.1 (0.07, 0.13)	0.74 (0.6, 0.92)
Carazo et al.	100,000	1.41 (1.19, 1.72)	0.2 (0.01, 0.43)	0.35 (0.27, 0.42)	0.75 (0.62, 0.93)
	500,000	1.44 (1.19, 1.78)	0.21 (0.02, 0.46)	0.34 (0.26, 0.41)	0.77 (0.62, 0.95)
Laxminarayan et al.	100,000	2.44 (1.98, 3.23)	0.03 (0, 0.11)	0.04 (0.01, 0.08)	0.92 (0.69, 1)
	500,000	2.47 (1.99, 3.23)	0.03 (0, 0.11)	0.04 (0.01, 0.07)	0.92 (0.67, 1)
Dattner et al.	100,000	1.12 (0.65, 1.69)	0.63 (0.12, 1.06)	0.37 (0.21, 0.54)	0.65 (0.45, 0.91)
	500,000	1.06 (0.65, 1.55)	0.57 (0.1, 1)	0.38 (0.24, 0.54)	0.63 (0.43, 0.88)

Appendix 1—table 8

Simulation study for validating the estimates and the corresponding power.

Parameter	Simulation value	Mean estimate	Proportion covered (over 50)
Lyngse et al.
$σ_{v a r}$ : Infectiousness variation	1.48	1.57	0.94
$λ_{c}$ : hazard of infection from outside the household (10^–2)	0.06	0.12	0.88
$λ_{h}$ : hazard of infection from an infected household member	0.11	0.09	0.92
$β :$ relationship between number of household contacts and transmission rate	0.72	0.75	0.96
Carazo et al.
$σ_{v a r}$ : Infectiousness variation	1.41	1.49	0.94
$λ_{c}$ : hazard of infection from outside the household (10^–2)	0.2	0.24	0.96
$λ_{h}$ : hazard of infection from an infected household member	0.35	0.33	0.92
$β :$ relationship between number of household contacts and transmission rate	0.75	0.77	0.96
Laxminarayan et al.
$σ_{v a r}$ : Infectiousness variation	2.44	2.6	0.94
$λ_{c}$ : hazard of infection from outside the household (10^–2)	0.03	0.05	0.96
$λ_{h}$ : hazard of infection from an infected household member	0.04	0.03	0.9
$β :$ relationship between number of household contacts and transmission rate	0.92	0.82	1
Dattner et al.
$σ_{v a r}$ : Infectiousness variation	1.12	1.18	0.92
$λ_{c}$ : hazard of infection from outside the household (10^–2)	0.63	0.69	0.92
$λ_{h}$ : hazard of infection from an infected household member	0.37	0.36	0.96
$β :$ relationship between number of household contacts and transmission rate	0.65	0.68	0.98

Appendix 1—table 9

A sensitivity analysis of using normal distribution (main analysis) instead of lognormal distribution (sensitivity analysis) for individual infectiousness.

Article	Model	Estimates of infectiousness variation	Estimates of probability of infection from community (10^–2)	Estimates of probability of infection from household	Relationship between transmission and number of contacts ( $β)$	Difference in DIC
Lyngse et al.	Main analysis	1.48 (1.29, 1.7)	0.06 (0, 0.16)	0.11 (0.08, 0.13)	0.72 (0.59, 0.89)
	Sensitivity analysis	0.93 (0.84, 1.03)	0.03 (0, 0.11)	0.06 (0.05, 0.07)	0.7 (0.58, 0.83)	2821
Carazo et al.	Main analysis	1.41 (1.19, 1.72)	0.2 (0.01, 0.43)	0.35 (0.27, 0.42)	0.75 (0.62, 0.93)
	Sensitivity analysis	1.05 (0.92, 1.21)	0.06 (0, 0.24)	0.18 (0.16, 0.2)	0.71 (0.59, 0.84)	2569
Laxminarayan et al.	Main analysis	2.44 (1.98, 3.23)	0.03 (0, 0.11)	0.04 (0.01, 0.08)	0.92 (0.69, 1)
	Sensitivity analysis	1.31 (1.14, 1.48)	0.02 (0, 0.08)	0.05 (0.03, 0.06)	0.91 (0.66, 1)	818
Dattner et al.	Main analysis	1.12 (0.65, 1.69)	0.63 (0.12, 1.06)	0.37 (0.21, 0.54)	0.65 (0.45, 0.91)
	Sensitivity analysis	0.66 (0.47, 0.88)	0.3 (0.02, 0.71)	0.18 (0.13, 0.22)	0.56 (0.4, 0.75)	908

Appendix 1—table 10

Summary of characteristic of identified studies.

SD: standard deviation.

Article	Number of households	Number of contacts	Number of secondary cases	Mean number of contacts	SD of number of contact	Secondary attack rate (SAR)	SD of number of secondary cases ( $σ_{s e c}$ )
Lyngse et al.	6782	14,233	1902	2.1 (2.07, 2.13)	1.17 (1.15, 1.19)	0.13 (0.13, 0.14)	0.6 (0.59, 0.61)
Carazo et al.	3727	8460	2574	2.27 (2.23, 2.31)	1.19 (1.16, 1.21)	0.3 (0.29, 0.31)	0.97 (0.95, 0.99)
Laxminarayan et al.	915	3113	283	3.4 (3.28, 3.53)	1.94 (1.86, 2.04)	0.09 (0.08, 0.1)	0.81 (0.77, 0.85)
Dattner et al.	591	2211	720	3.74 (3.54, 3.94)	2.5 (2.36, 2.65)	0.33 (0.31, 0.35)	1.6 (1.51, 1.7)
Layan et al.	208	670	264	3.22 (3.01, 3.44)	1.58 (1.45, 1.75)	0.39 (0.36, 0.43)	1.59 (1.45, 1.76)
Hart et al.	172	433	194	2.52 (2.34, 2.69)	1.16 (1.05, 1.29)	0.45 (0.4, 0.5)	1.11 (1, 1.24)
Hubiche et al.	103	291	119	2.83 (2.6, 3.05)	1.18 (1.04, 1.37)	0.41 (0.35, 0.47)	1.14 (1, 1.32)
Wilkinson et al.	95	220	26	2.32 (2.02, 2.61)	1.47 (1.28, 1.71)	0.12 (0.08, 0.17)	0.66 (0.58, 0.77)
Tsang et al.	47	189	38	4.02 (3.39, 4.66)	2.22 (1.85, 2.79)	0.2 (0.15, 0.27)	1.31 (1.09, 1.65)
Reukers et al.	55	187	78	3.4 (3.11, 3.69)	1.1 (0.93, 1.35)	0.42 (0.35, 0.49)	1.33 (1.12, 1.64)
Han et al.	55	185	78	3.36 (3.08, 3.65)	1.08 (0.91, 1.33)	0.42 (0.35, 0.5)	1.27 (1.07, 1.57)
Méndez-Echevarría et al.	63	174	57	2.76 (2.57, 2.95)	0.78 (0.66, 0.94)	0.33 (0.26, 0.4)	0.96 (0.82, 1.17)
Dutta et al.	32	170	55	5.31 (4.52, 6.1)	2.28 (1.83, 3.03)	0.32 (0.25, 0.4)	1.59 (1.28, 2.12)
Koureas et al.	32	153	50	4.78 (3.94, 5.62)	2.43 (1.95, 3.23)	0.33 (0.25, 0.41)	2.14 (1.72, 2.84)
Bernardes-Souza et al.	40	112	55	2.8 (2.33, 3.27)	1.51 (1.23, 1.93)	0.49 (0.4, 0.59)	1.48 (1.21, 1.9)
Posfay-Barbe et al.	39	111	46	2.85 (2.54, 3.16)	0.99 (0.81, 1.27)	0.41 (0.32, 0.51)	0.94 (0.77, 1.21)
Hsu et al.	38	96	49	2.53 (2.12, 2.93)	1.27 (1.03, 1.64)	0.51 (0.41, 0.61)	0.87 (0.71, 1.12)

Appendix 1—table 11

Association between infectiousness variation estimated from household transmission models, and other statistics from 17 household studies, based on meta-regression.

Statistic	Infectiousness variation ( $σ_{v a r}$ *)	Standard deviation (SD) of the distribution of number of secondary cases ( $σ_{s e c}$ )	Secondary attack rate (SAR)
Pooled estimates	1.33 (0.95, 1.70)	1.19 (1.03, 1.35)	0.35 (0.28, 0.44)
I²	78.4	99.2	99.1
Factors
Estimate	β	β	exp (β)
Mean number of contacts	0.31 (−0.16, 0.78)	0.35 (0.22, 0.48)	1.09 (0.83, 1.43)
SD number of contacts	0.55 (−0.12, 1.21)	0.42 (0.15, 0.69)	0.80 (0.51, 1.25)
Implementation of lockdown	0.16 (−0.61, 0.93)	–0.06 (−0.40, 0.28)	0.69 (0.43, 1.10)
Index cases are confirmed by PCR only	0.48 (−0.32, 1.29)	0.02 (−0.33, 0.38)	1.09 (0.65, 1.85)
Secondary cases are confirmed by PCR only	0.78 (0.13, 1.43)	0.03 (−0.30, 0.35)	0.88 (0.55, 1.41)
Only ancestral strains are circulating in study period	0.76 (−0.03, 1.55)	0.07 (−0.31, 0.45)	0.75 (0.43, 1.30)
All household contacts were tested	0.03 (−0.87, 0.93)	0.28 (−0.04, 0.59)	0.96 (0.58, 1.58)

*

Estimates based on results from 14 studies

Appendix 1—table 12

Pooled estimates for duration of viral shedding for COVID-19 from 11 systematic reviews.

Study	Sampling site	Laboratory method	Pooled estimates (mean/median)	95% CI	Range	I²
Cevik	Upper respiratory tract	PCR	17.0	15.5–18.6	6.0–53·9
Cevik	Lower respiratory tract	PCR	14.6	9.3–20.0	6.2–22.7	97%
Cevik	Stool	Viral culture	17.2	14.4–20.1	9.8–27.9	96.6%
Cevik	Serum/blood	Viral culture	16.6	3.6–29.7	10.0–23.3	99%
Fontana	Respiratory sources	PCR	18.4*	15.5–21.3	5.5–53.5	98.87%
Fontana	Rectal/stool	PCR	22.1*	14.4–29.8	11–33	95.86%
Okita	Upper respiratory tract (nasal swab+throat swab)	PCR	18.29	17.00–19.89	8.33–39.97	99%
Okita	Sputum	PCR	23.79	20.43–27.16	15.50–32.00	93%
Okita	Blood	PCR	14.60	12.16–17.05	11.00–17.58	88%
Okita	Stool	PCR	22.38	18.40–26.35	10.67–51.40	97%
Qutub	Respiratory tract	Viral culture	28.75/11**	8.5–14.5
Rahmani	Respiratory tract	PCR	27.90	23.27–32.52	7.40–132.00	99.1%
Xu	Respiratory tract (symptomatic cases)	PCR	11.1±5.8***		0–24
Xu	Gastrointestinal tract (symptomatic cases)	PCR	23.6±8.8***		10–33
Yan	Unrestricted	PCR	16.8	14.8–19.4		99.56%
Yan	Stool	PCR	30.3	23.1–39.2		92.09%
Yan	Respiratory tract	PCR	17.5	14.9–20.6		99.67%
Yan	Upper respiratory tract	PCR	17.5	14.6–21.0		99.53%
Diaz	Stool	PCR	22*	19–25
Chen	(Asymptomatic infections)		14.14*	11.25–17.04	11.00–17.25
Li	Upper respiratory tract (nasopharyngeal/throat swabs)	PCR	11.43	10.1–12.77		75.3%
Zhang	Stool	PCR	21.8	16.4–27.1
Zhang	Respiratory tract	PCR	14.7	9.9–19.5

*

Median estimate, **median/grouped median, ***this study analyzed by cases, and reported mean ± SD.

Appendix 1—table 13

Pooled estimates for duration of viral shedding for COVID-19 in subgroups from seven systematic reviews.

Study	Sampling site (subgroups)	Laboratory method	Pooled estimates (mean/median)	95% CI	Range	I²
Fontana	Respiratory sources (among severely ill patients)	PCR	19.8*	16.2–23.5	11–31	96.42%
Fontana	Respiratory sources (in mild-to-moderate illness)	PCR	17.2*	14.0–20.5	8–25	95.64%
Okita	Upper respiratory tract (nasal swab)	PCR	19.34	16.60–22.07		99%
Okita	Upper respiratory tract (throat swab)	PCR	17.85	16.43–19.26		98%
Okita	Upper respiratory tract (age < 60)	PCR	16.95	13.56–20.35	8.62–35.67	98%
Okita	Upper respiratory tract (age ≥ 60)	PCR	21.24	14.06–28.41	8.25–40.33	99%
Okita	Upper respiratory tract (with comorbidities)	PCR	20.26	17.60–22.92	9.67–34.00	93%
Okita	Upper respiratory tract (without comorbidities)	PCR	14.66	12.63–16.69	10.82–27.25	85%
Okita	Upper respiratory tract (severe patients)	PCR	20.79	18.03–23.55	14.00–38.33	98%
Okita	Upper respiratory tract (nonsevere patients)	PCR	16.36	14.07–18.66	8.00–37.33	99%
Okita	Upper respiratory tract (severe patients) (for studies with mean age ≥ 40 + comorbidity > 30%)	PCR	21.53	17.57–25.50	14.00–29.50	91%
Okita	Upper respiratory tract (severe patients) (for studies with mean age ≥ 40 + comorbidity >30%)	PCR	20.08	15.87–24.29	13.12–33.67	100%
Okita	Upper respiratory tract (treated with glucocorticoid)	PCR	19.72	17.92–21.52	13.87–33.67	92%
Okita	Upper respiratory tract (treated without glucocorticoid)	PCR	15.64	14.18–17.10	8.33–31.60	96%
Okita	Upper respiratory tract (treated with glucocorticoid) (for studies with mean age: 30–60+comorbidity > 50%)	PCR	21.98	16.48–27.48	14.25–33.67	94%
Okita	Upper respiratory tract (treated without glucocorticoid) (for studies with mean age: 30–60+comorbidity > 50%)	PCR	16.14	12.60–19.68	13.22–24.44	92%
Okita	Upper respiratory tract (Asian)	PCR	18.10	16.95–19.25	8.33–34.75	98%
Okita	Upper respiratory tract (European)	PCR	19.27	11.59–26.95	8.50–39.97	100%
Okita	Upper respiratory tract (Asian) (for studies with mean age ≥ 40 + comorbidity >40%)	PCR	20.66	18.18–23.14	12.00–32.00	96%
Okita	Upper respiratory tract (European) (for studies with mean age ≥ 40 + comorbidity > 40%)	PCR	23.68	10.85–36.51	13.00–39.97	100%
Qutub	Respiratory tract (severe patients)	Viral culture	47.5/20**	9.0–53.0
Qutub	Respiratory tract (severe patients were not specified of excluded)	Viral culture	10/9**	8.0–13.0
Qutub	Respiratory tract (immunocompromised patients)	Viral culture	54.36/20**	9.0–85.98
Qutub	Respiratory tract (immunocompromised patients were not specified of excluded)	Viral culture	11.67/9**	8.2–13.3
Rahmani	Not specific (immunocompetent individuals)	PCR	26.54	21.44–31.64	7.40–91.20	99.3%
Rahmani	Not specific (immunocompromised individuals)	PCR	36.28	21.93–50.63	15.90–132.00	94.2%
Xu	Respiratory tract (asymptomatic cases)	PCR	9.4±5.1***
Xu	Gastrointestinal tract (asymptomatic cases)	PCR	16.8±9.8***
Yan	Unrestricted (symptomatic cases)	PCR	19.7	17.2–22.7		99.34%
Yan	Unrestricted (asymptomatic cases)	PCR	10.9	8.3–14.3		98.89%
Yan	Unrestricted (severe patients)	PCR	24.3	18.9–31.1		91.88%
Yan	Unrestricted (nonsevere patients)	PCR	22.8	16.4–32.0		99.81%
Yan	Unrestricted (females)	PCR	19.4	9.5–39.4		93.93%
Yan	Unrestricted (males)	PCR	11.9	8.4–16.9		87.83%
Yan	Unrestricted (adults)	PCR	23.2	19.0–28.4		99.24%
Yan	Unrestricted (children)	PCR	9.9	8.1–12.2		85.74%
Yan	Unrestricted (with chronic diseases)	PCR	24.2	19.2–30.2		84.07%
Yan	Unrestricted (without chronic diseases)	PCR	11.5	5.3–25.0		82.11%
Yan	Unrestricted (treated with corticosteroid)	PCR	28.3	25.6–31.2		0.00%
Yan	Unrestricted (treated without corticosteroid)	PCR	16.2	11.5–22.5		92.27%
Yan	Unrestricted (antiviral treatment)	PCR	17.6	13.4–22.2		98.99%
Yan	Unrestricted (mono-antiviral treatment)	PCR	21.2	15.3–29.2		90.04%
Yan	Unrestricted (multiantiviral treatment)	PCR	20.3	13.7–30.3		99.46%
Chen	Unrestricted (asymptomatic infections)	PCR or serum antibody	14.14*	11.25–17.04	11.00–17.25

*

Median estimate, **median/grouped median, ***this study analyzed by cases, and reported mean ± SD.

Appendix 1—table 14

Pooled estimates for duration of infectious period for COVID-19 in subgroups from two systematic reviews.

Study	Sampling site (subgroups)	Laboratory method	Pooled estimates	95% CI	Range	I²
Rahmani	Replicant competent virus isolation	Viral culture	7.27	5.70–8.84	3.40–89.00	92.2%
Wang	Not specific	Not specific	6.25	5.09–7.51
Rahmani	Replicant competent virus isolation (immunocompetent individuals)	Viral culture	6.33	4.92–7.75	3.00–13.00	92.4%
Rahmani	Replicant competent virus isolation (immunocompromised individuals)	Viral culture	29.50	12.46–46.53	13.80–89.00	84.8%

Appendix 1—table 15

Probability distributions of the incubation period and relative infectivity levels during the infectious period.

For the infectious period, day 0 corresponds to the symptom onset day. These two distributions are used to generate the infectiousness profile since infections.

Day	Incubation period		Infectious period
Day	Mean = 5 days	Day	Max = 13 days
1	0.058	−5	1.0
2	0.11	−4	1.0
3	0.14	−3	1.0
4	0.16	−2	1.0
5	0.15	−1	1.0
6	0.13	0	1.0
7	0.10	1	1.0
8	0.068	2	1.0
9	0.044	3	0.8
10	0.026	4	0.6
11	0.014	5	0.4
12	0.0072	6	0.2
13	0.0034	7	0.1
14	0.0015	8

Author response table 1

Study	Pearson’s correlation	Shearman’s correlation
Lyngse, et al.	0.00 (-0.02, 0.03)	0.00 (-0.03, 0.02)
Carazo, et al.	0.00 (-0.03, 0.04)	0.00 (-0.03, 0.03)
Laxminarayan, et al.	0.00 (-0.07, 0.05)	-0.02 (-0.08, 0.03)
Dattner, et al.	0.01 (-0.07, 0.09)	0.00 (-0.08, 0.09)

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Tim K Tsang
Xiaotong Huang
Can Wang
Sijie Chen
Bingyi Yang
Simon Cauchemez
Benjamin John Cowling

(2023)

The effect of variation of individual infectiousness on SARS-CoV-2 transmission in households

eLife 12:e82611.

https://doi.org/10.7554/eLife.82611

Figures

Summary of statistics for 17 identified studies.

Modeling results of household transmission dynamics and infectiousness variation.

Estimate distribution of relative infectiousness based on the pooled estimate.

Relationship between infectiousness variation and statistic.

Process of systematic review.

Correlation plots for the posterior distribution of model parameters in Lyngse et al., Carazo et al., Laxminarayan et al., and Dattner et al.

The density plot of the distribution of infectiousness profile since infections, used in the modeling analysis.

Tables

Summary of characteristic of identified studies.

Summary of model estimates.

Model adequacy check for Lyngse et al.

Model adequacy check for Carazo et al.

Model adequacy check for Laxminarayan et al.

Model adequacy check for Dattner et al.

Comparison of model estimates from 100k Markov chain Monte Carlo (MCMC) iterations and 500k MCMC iterations.

Simulation study for validating the estimates and the corresponding power.

A sensitivity analysis of using normal distribution (main analysis) instead of lognormal distribution (sensitivity analysis) for individual infectiousness.

Summary of characteristic of identified studies.

Association between infectiousness variation estimated from household transmission models, and other statistics from 17 household studies, based on meta-regression.

Pooled estimates for duration of viral shedding for COVID-19 from 11 systematic reviews.

Pooled estimates for duration of viral shedding for COVID-19 in subgroups from seven systematic reviews.

Pooled estimates for duration of infectious period for COVID-19 in subgroups from two systematic reviews.

Probability distributions of the incubation period and relative infectivity levels during the infectious period.

Additional files

MDAR checklist

Download links

Downloads (link to download the article as PDF)

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Summary of statistics for 17 identified studies.

Modeling results of household transmission dynamics and infectiousness variation.

Estimate distribution of relative infectiousness based on the pooled estimate.

Relationship between infectiousness variation and statistic.

Process of systematic review.

Correlation plots for the posterior distribution of model parameters in Lyngse et al., Carazo et al., Laxminarayan et al., and Dattner et al.

The density plot of the distribution of infectiousness profile since infections, used in the modeling analysis.

Summary of characteristic of identified studies.

Summary of model estimates.

Model adequacy check for Lyngse et al.

Model adequacy check for Carazo et al.

Model adequacy check for Laxminarayan et al.

Model adequacy check for Dattner et al.

Comparison of model estimates from 100k Markov chain Monte Carlo (MCMC) iterations and 500k MCMC iterations.

Simulation study for validating the estimates and the corresponding power.

A sensitivity analysis of using normal distribution (main analysis) instead of lognormal distribution (sensitivity analysis) for individual infectiousness.

Summary of characteristic of identified studies.

Association between infectiousness variation estimated from household transmission models, and other statistics from 17 household studies, based on meta-regression.

Pooled estimates for duration of viral shedding for COVID-19 from 11 systematic reviews.

Pooled estimates for duration of viral shedding for COVID-19 in subgroups from seven systematic reviews.

Pooled estimates for duration of infectious period for COVID-19 in subgroups from two systematic reviews.

Probability distributions of the incubation period and relative infectivity levels during the infectious period.

MDAR checklist

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)