Characterizing transmission is critical to control the spread of an emerging infectious disease. The reproductive number is the widely adopted measure of infectiousness. However, it only measures the average number of secondary cases infected by an infected person, not the heterogeneity in the number of transmissions. Variation of individual infectiousness is particularly highlighted by superspreading events (SSEs), in which a minority of cases are responsible for a majority of transmission events. Such phenomena, illustrated by the ‘80/20 rule’ (i.e., 20% of cases responsible for 80% transmission; Adam et al., 2020; Sun et al., 2021), have been observed in emerging infectious disease outbreaks (Lloyd-Smith et al., 2005), including severe acute respiratory syndrome (SARS) (Shen et al., 2004), Middle East respiratory syndrome (Cauchemez et al., 2016; Cowling et al., 2015), and most recently the COVID-19 pandemic (Adam et al., 2020; Lau et al., 2020; Sun et al., 2021; Wong and Collins, 2020; Zhao et al., 2021). In these outbreaks, the proportion of cases attributed to 80% transmission, and the dispersion parameter that is estimated by fitting the negative binomial distribution to the number of secondary cases (Lloyd-Smith et al., 2005), are considered as measures of transmission heterogeneity.

However, the number of contacts per index cases is often not reported in SSE studies, and hence not incorporated in the analyses. In addition, SSE studies usually analyze clusters from different settings, in which the baseline transmission risk and density of exposure could be different (Thompson, 2021). Finally, studies of transmission heterogeneity that focus on SSEs described in the literature may suffer from publication bias, with larger clusters having higher probability of being observed and reported (Zhao et al., 2021). Therefore, the observed heterogeneity in the number of secondary cases could be the result of large number of contacts in SSE settings, or confounding from these factors (Althouse et al., 2020; Bagdasarian and Fisher, 2020), instead of variation in individual infectiousness.

Households are one of the most important settings for SARS-CoV-2 transmission, with 4- to 10-fold higher transmission risk than other places (Thompson, 2021). Hence, household transmission studies provide an ideal setting to quantify variations in individual infectiousness. In a household transmission study, an index case is identified, and their household contacts are followed up for 1–2 weeks, during which there is high transmission potential (Tsang et al., 2016). Therefore, the number of contacts is known while transmission risks and reporting biases can be controlled. We aim to characterize the variation of individual infectiousness by analyzing data from household transmission studies.

We conducted a systematic review to gather information on the number of secondary cases with the number of household contacts for each household, in the form of number of households with X cases among households of size Y. In total, we identified 17 studies, comprising 13,098 index cases and 31,359 household contacts (Appendix 1—figure 1, Appendix 1—table 1; Bernardes-Souza et al., 2021; Carazo et al., 2022; Dattner et al., 2021; Han et al., 2022; Hart et al., 2022; Hsu et al., 2021; Hubiche et al., 2021; Koureas et al., 2021; Laxminarayan et al., 2020; Layan et al., 2022; Lyngse et al., 2022; Méndez-Echevarría et al., 2021; Posfay-Barbe et al., 2020; Reukers et al., 2021; Wilkinson et al., 2021). Most studies covered a period from January to November 2020, which was dominated by ancestral strains, except for Layan et al. (from December 2020 to April 2021) and Hsu et al. (from January 2020 to February 2021), which covered both ancestral strains and the alpha variant.

We then developed a statistical model to quantify the degree and the impact of variation of infectiousness of cases on transmission dynamics. The individual-based household transmission model describes the probability of infection of household contacts as depending on the time since infection in other infected persons in the household, so that infections from outside the household (community infections), or infections via other household contacts rather than the index case (tertiary infections) are allowed (Cauchemez et al., 2009; Tsang et al., 2014; Tsang et al., 2021). Therefore, the model could estimate the per-contact hazard of infection, which implicitly controls for number of household contacts in households. We extend this model by adding a random effect (${\delta }_i$) on the individual infectiousness of cases. Here, the relative infectiousness of case i compared with case j is exp(${\delta }_i$)/exp(${\delta }_j$). The parameter for variation in individual infectiousness (hereafter denoted as infectiousness variation, ${\sigma }_{var}$) is the standard deviation (SD) of the random effect characterizing individual infectiousness, so that ${\delta }_i$ follows a normal distribution with mean equal to 0 and SD equal to ${\sigma }_{var}$ .

We separately fit the models to 14 studies with more than 150 contacts (Carazo et al., 2022; Dattner et al., 2021; Dutta et al., 2020; Han et al., 2022; Hart et al., 2022; Hubiche et al., 2021; Koureas et al., 2021; Laxminarayan et al., 2020; Layan et al., 2022; Lyngse et al., 2022; Méndez-Echevarría et al., 2021; Reukers et al., 2021; Tsang et al., 2022; Wilkinson et al., 2021; Figure 1, Appendix 1—table 2). For 12 studies out of 14, models with infectiousness variation perform substantially better (range of ∆DIC: 5.8–268) (Figure 2, Appendix 1—table 2). From these 12 studies, the estimated infectiousness variation (${\sigma }_{var})$ ranged from 1.03 to 2.83. This suggests that, the 20% most infectious cases are 2.4- to 10-fold more infectious than the average case. Based on the two largest studies with 6782 and 3727 households (Carazo et al., 2022; Lyngse et al., 2022), the estimated infectiousness variation is 1.48 (95% credible interval [CrI]: 1.29, 1.7) and 1.41 (95% CrI: 1.19, 1.72), suggesting that, among all cases, the 20% most infectious are 3.5-fold (95% CrI: 3.0- to 4.2-fold) and 3.3-fold (95% CrI: 2.7- to 4.3-fold) more infectious than the average case. The estimated daily probability of infection from outside the household and estimated person-to-person transmission probability within households range from 0.0003 to 0.017, and from 0.06 to 0.51, respectively. The estimates of parameters for the relationship between number of contacts and transmission (larger value indicates stronger inverse association) range from 0.43 to 0.92, except for the study by Layan et al., 2022, where it is equal to 0.2. For all studies, the predicted final size distribution is consistent with the observed data and the model fit is judged adequate (Appendix 1—Tables 3–7, Appendix 1—figure 2). Simulation studies demonstrated that there is no important systematic bias, with 88–100% (depending on the parameter) of the 95% credible intervals covering the simulation value (Appendix 1—table 8). This suggests that the algorithm could estimate adequately the posterior distribution. We conduct a sensitivity analysis that assumes the individual infectiousness of cases follows a Gamma distribution, but the fit worsens substantially (Appendix 1—table 9).

Figure 1

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Figure 2

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We conduct random effects meta-analyses on estimates of individual infectiousness from the 14 identified studies. The pooled estimate of infectiousness variation is 1.33 (95% confidence interval [CI]: 0.95, 1.70), suggesting that the 20% most infectious cases are 3.1-fold (95% CI: 2.2- to 4.2-fold) more infectious than the average case (Figure 3). Based on this fitted distribution, we estimate that 5.9% (95% CI: 1.4%, 11.1%) and 14.9% (95% CI: 7.2%, 20.7%) of cases could be at least 8- and 4-fold more infectious than average cases, respectively.

Figure 3

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We further explore if the secondary attack rate (SAR, the proportion of infected contacts), and the SD of the distribution of number of secondary cases (${\sigma }_{sec})$ (Figure 4; Appendix 1—table 10) may be correlated with the infectiousness variation. In meta-regression, we find the infectiousness variation is associated with SAR (Appendix 1—table 11). We estimate that doubling SAR are associated with 0.55 (95% CI: 0.21, 0.89) unit decrease in infectiousness variation, with R-squared equal to 67% respectively. In addition, we find that higher infectiousness variation is associated with only using PCR to ascertain secondary cases. Regarding other statistics, we find that ${\sigma }_{sec}$ is positively associated with mean and SD of number of contacts. Other than these associations, we find no association between these statistics and implementation of lockdown, ascertainment method of index and secondary cases, and the circulating virus of SARS-CoV-2 in the study period.

Figure 4

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In this study, we characterize the impact of variation of individual infectiousness on heterogeneity of transmission of COVID-19 in households. We demonstrate that it can be estimated from household data using a modeling approach. The pooled estimate of infectiousness variation from 14 studies suggests that the 20% most infectious cases have 3.1-fold (95% CI: 2.2- to 4.2-fold) higher infectiousness compared with average index cases. This implies there is substantial variation in individual infectiousness of cases in households. Given that we focused our analysis on households with known number of contacts in studies conducted in the early outbreaks caused by ancestral strains, the estimated infectiousness variations are corrected for the variations caused by number of contacts and transmission risks in different settings, difference in pre-existing immunity among contacts (almost everyone is naïve and unvaccinated), and the difference in transmissibility among variants. Hence, this estimated infectiousness variation measures the variation caused by difference in individuals, which may be contributed by both biological factors and host behaviors, but not other potential confounding factors mentioned above.

Regarding host behaviors, multiple contact patterns, particularly by age, could contribute to the variations in infectiousness of cases. For example, mother-child contacts are usually more intense than father-child contacts, and adult cases are more capable of self-isolation within a household compared with children. Furthermore, contact pattern studies suggested that school-age children and young adults tended to mix with people of the same age (Mossong et al., 2008; Mousa et al., 2021). Also, the duration of contact could vary, which could also contribute to the variations in infectiousness of cases (Toth et al., 2015). It should be noted that contacts have different features, including their number, frequency, and duration that may contribute to variations in infectiousness. Previous studies also suggest that the relative importance of contact characteristics on transmission may be different among viruses (De Cao et al., 2014). Individual behaviors may also be influenced by control measures and recommendation from public health agencies. For example, lockdown and stay-at-home orders may increase the time spending at home. Mask-wearing when in contact with other household members, using separate bedrooms and bathrooms, avoiding having meals together may reduce the transmission in households (Ng et al., 2021). Also, social disparity such as occupation may increase or reduce the risk of transmission in households, including the availability of personal protective equipment (PPE), or being healthcare worker (Yang et al., 2021). These factors may have impact of the transmission risk and hence SAR in households. In addition, heterogeneity in these different factors may have contributed infectiousness variation.

Biological factors may also contribute to such variations. For example, the SAR for index cases with fever and cough are 1.4- and 1.3-fold higher than index cases without fever and cough, respectively (Madewell et al., 2021). Viral shedding is used as a proxy measure of infectiousness, and consistently it also has substantial variations, as suggested by 11 systematic reviews (Appendix 1—Tables 12–14). Regarding the magnitude of viral shedding, studies report high variations of temporal viral shedding patterns among individuals (He et al., 2020; Jones et al., 2021; Sun et al., 2022). In addition, the duration of viral shedding can be highly heterogeneous, with pooled estimates of mean durations ranging from 11.1 to 30.3 days, and almost all reviews reporting high heterogeneity of estimates (Cevik et al., 2021; Chen et al., 2021b; Díaz et al., 2022; Fontana et al., 2021; Li et al., 2020b; Okita et al., 2022; Qutub et al., 2022; Rahmani et al., 2022; Xu et al., 2020; Yan et al., 2021; Zhang et al., 2021). Such heterogeneities still exist in subgroup analyses by age and severity (Cevik et al., 2021; Fontana et al., 2021; Okita et al., 2022; Qutub et al., 2022; Rahmani et al., 2022; Xu et al., 2020; Yan et al., 2021). The infectious period, proxied by duration of replicant competent virus isolation, is also heterogeneous (Rahmani et al., 2022; Appendix 1—table 14). One review also suggests that heterogeneity in viral shedding is an intrinsic virological factor facilitating higher dispersion parameter for SARS-CoV-2 if we compare it with the corresponding patterns in SARS-CoV-1 and pandemic influenza A(H1N1)pdm09 (Chen et al., 2021a).

The observed variation in individual infectiousness is consistent with past analyses of the dispersion parameter in a negative binomial distribution fitted to number of secondary cases per index case of COVID-19 (Sun et al., 2021; Wong et al., 2015). However, in these studies, the number of contacts was not considered. Therefore, the observed variations may not apply directly to households with limited number of contacts. It should be noted that the SD of the distribution of number of secondary cases (${\sigma }_{sec}$) is only weakly correlated with infectiousness variation. This is because ${\sigma }_{sec}$ is highly correlated with the mean and SD of the number of contacts, suggesting that it may depend on distribution of number of contacts, and hence may not be comparable among studies. Infectiousness variation is also correlated with the SAR. When SAR is higher, it is expected that more contacts are infected and therefore the observed number of secondary cases is less heterogeneous (Adam et al., 2022). We find higher infectiousness variation is associated with only using PCR to confirm secondary cases. One potential reason is that using other methods may lower the sensitivity of detecting infection, resulting in lower estimates of SAR and hence higher estimates of infectiousness variation. Further investigations are needed to explore roles of other potential factors affecting infectiousness variation, such as contact frequency among different regions (Mousa et al., 2021).

An important limitation of our study is that we do not have individual-level data. Therefore, we are unable to determine the impact of demographic factors like age and sex on infectiousness variation. Also, we cannot disentangle the host behaviors from biological factors. Previous analysis suggested no evidence of the impact of age on infectiousness of cases (Lau et al., 2020; Sun et al., 2021). In addition, we could not include factors affecting susceptibility to infection. Our estimates of infectiousness variation should be interpreted in light of these limitations: they capture heterogeneity in infectiousness due to demographic, host, and biological factors. However, in one study that included susceptibility component in the estimation of individual infectiousness, substantial heterogeneity remained with 20% of cases estimated to contribute to 80% of transmission (Tsang et al., 2022). Second, the recruitment methods among studies are different. This may affect the comparability of the results, although all index cases are laboratory-confirmed in all studies (Tsang et al., 2021). Third, we assumed that risks of infection from community for all households are the same, but there were different factors that may affecting this, including occupations, such as healthcare workers, social economic status that related to assess to PPEs (Yang et al., 2021). Finally, most of our identified studies were conducted in the period of circulation of ancestral strains, and therefore the identified infectiousness variation may not be directly applicable to other variants.

In conclusion, we developed a modeling approach to estimate variation in individual infectiousness from household data. Result indicates that there is substantial variation in individual infectiousness, which is important for epidemic management.

The data and computer code (in R language) for conducting the data analysis can be downloaded from https://github.com/timktsang/covid19_transmission_heterogeneity (copy archived at swh:1:rev:634390fa66a4bfb998da691e7cd81cf45e38c6db).

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Author details

1. Tim K Tsang

   1. WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China
   2. Laboratory of Data Discovery for Health, Hong Kong, China

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing – review and editing

   For correspondence

   timtsang@connect.hku.hk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5037-6776

2. Xiaotong Huang

   WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

   Contribution

   Data curation, Investigation, Visualization

   Competing interests

   No competing interests declared

3. Can Wang

   WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

   Contribution

   Data curation, Investigation

   Competing interests

   No competing interests declared

4. Sijie Chen

   WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

   Contribution

   Investigation, Visualization

   Competing interests

   No competing interests declared

5. Bingyi Yang

   WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

   Contribution

   Writing – review and editing

   Competing interests

   No competing interests declared

6. Simon Cauchemez

   Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Paris, France

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Writing – review and editing

   Contributed equally with

   Benjamin John Cowling

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9186-4549

7. Benjamin John Cowling

   Laboratory of Data Discovery for Health, Hong Kong, China

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Writing – review and editing

   Contributed equally with

   Simon Cauchemez

   For correspondence

   bcowling@hku.hk

   Competing interests

   consults for AstraZeneca, Fosun Pharma, GlaxoSmithKline, Moderna, Pfizer, Roche and Sanofi Pasteur. The authors report no other potential conflicts of interest

   "This ORCID iD identifies the author of this article:" 0000-0002-6297-7154

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