The study protocol was approved by the University of Guelph Research Ethics Board (protocol #20–04-011) and the University of Toronto Research Ethics Board (protocol #38251). The research company, Dynata (https://www.dynata.com), was contracted to conduct four cross-sectional electronic surveys in Canadians over the age of 18 years from May 7–19 (Survey 1), July 17–27 (Survey 2), September 21–October 10 (Survey 3), and December 8–31 (Survey 4). No effort was made to recontact previous respondents for each subsequent survey. A quota sampling design was used to ensure the sample was representative of the Canadian population. Quotas for each survey were set for age, gender, official language and geographic region (i.e., Atlantic, Quebec, Ontario, and West) based on 2016 Canadian Census data . Participants were recruited from a panel of survey respondents and paid a nominal amount for completing the survey. Panelists who logged into their Dynata account during the study period were directed to the survey if they fit the quotas being targeted. Enrollment into the survey within each stratum was on a first-come, first-served basis. Survey responses were excluded from analysis if the survey was completed in less than one-third of the estimated completion time, if the respondent reported their age as less than 18 years, or if the survey was discontinued for exceeding the age, gender, or region quotas. Responses with duplicated entries for gender, age, postal code, date, and contact names were considered duplicate responses and removed from the dataset.
The survey instrument was adapted from the POLYMOD UK  and CoMix UK surveys . Respondents provided information about their age, gender, province of residence, and household composition and were then asked to record all direct contacts made between 5 am on the day preceding the survey and 5 am the day of survey completion including members of their household. A direct contact was defined as anyone who was met in person and with whom a short conversation occurred, or anyone with whom the respondent had physical contact [6, 11]. For each contact identified, respondents recorded the age of the contact and the setting in which the contact occurred. The survey instrument is available in the Additional file 1. As the contact diaries excluded people under the age of 18 years and with schools across the country reopening in September 2020, additional questions were added to Surveys 3 and 4. Respondents with children under 18 were asked whether any of the children in their household had attended school, taken the school bus, attended before/after school care, or participated in extracurricular activities in the 7 days prior to survey completion. Respondents were then asked to estimate the number of contacts each of their children had in each of these settings.
Given that schools had reopened, and many people were no longer working remotely by the time Survey 3 was deployed (September, 2020), respondents were also asked to identify whether their occupation required direct contact with more than 20 people during a typical work day. Respondents in these “high contact” occupations were asked to estimate the number of people in each age category with whom they would have contact at work on a typical work day. The number of reported contacts in Surveys 3 and 4 was truncated at 75 per respondent.
Respondents and contacts were categorized into age groups as follows: 18–29 years, 30–39 years, 40–49 years, 50–59 years, 60–69 years, and over 70 years. To ensure the sample was generally representative of the Canadian population, age, gender, region of residence, and household size of survey respondents were compared with the 2016 Canadian Census [16, 17]. Post-stratification weights were then calculated based on age and household size within Canadian region (Atlantic, Quebec, Ontario, West) using data from the 2016 Canadian census [16, 17].
The average number of contacts per respondent was calculated and stratified by age group, gender, household size, region of residence, and whether the contact diary was completed for a weekday or weekend day. The average number of contacts for each survey time period was compared to the POLYMOD UK study , which represents pre-pandemic contacts, by calculating the percent reduction from the mean number of contacts reported in POLYMOD.
Contact matrices were constructed for the age-specific mean number of contacts per 24-h period, adjusting for the age distribution in the Canadian population and reciprocity of contacts using the SocialMixr package in R . The 2016 Canadian census was used to correct for the probability of contact within the population . Missing contact age was sampled from other participants’ contacts within the same age group.
To provide a full contact matrix with which to estimate Rt, contacts for the 0–4 and 5–17 year age groups were imputed using a scaled version of the POLYMOD UK  data by multiplying the number of contacts in corresponding age groups from the POLYMOD UK  study by the ratio of the dominant eigenvalues of the POLYMOD UK and the observed matrices for all age groups surveyed in both studies, stratified by location of contact [11, 19]. As schools were closed during the data collection periods in Surveys 1 and 2, school contacts were removed from the POLYMOD UK  data for the analysis of these two surveys only.
Proportions were calculated for those who reported that at least one of the children in their household participated in school-based or extracurricular activities. The average number of contacts was calculated per child in different settings per day (school, aftercare, bus) or per week (extracurricular) among respondents reporting participation in these activities. These estimates were not included in the contact matrices.
The next generation matrix approach was used to estimate changes in the reproduction number (Rt) . The reproduction number was estimated by multiplying R0 prior to physical distancing interventions by the ratio of the dominant eigenvalues of the POLYMOD UK  and observed contact matrices under the assumptions of the social contact theory that the transmission rate is proportional to rate of social contacts [5, 20]. A meta-analysis reported that, prior to interventions, R0 followed a normal distribution with a mean of 2.6 and standard deviation of 0.54 .
To account for sampling variability and assess uncertainty, 10,000 bootstrapped samples were generated from each of the POLYMOD UK  and Survey 1–4 contact matrices. The ratio between the dominant eigenvalues were calculated for each bootstrapped sample of the POLYMOD UK  and each of the observed matrices providing a distribution of the relative change in Rt from the observed matrices and POLYMOD UK matrices . This distribution was scaled with the distribution of bootstrap samples to estimate Rt under physical distancing measures at each of the four survey time points.
The emergence of SARS-CoV-2 variants with increased transmissibility has the potential to require more stringent public health measures . To assess the theoretical impact of a more transmissible variant of SARS-CoV-2, each of the scaled estimates of Rt were multiplied by a factor of 1.56 to provide a distribution of Rt estimates consistent with a 56% increase in transmissibility .
The sensitivity of the estimates of Rt to changes in child-related contacts was assessed using previously published methods [11, 19]. As contact diary data were collected from adults only, there is uncertainty about the average number of child-to-child and child-to-adult contacts under COVID-19 public health measures. To estimate the impact of varying the levels of child-related contacts on the estimates of Rt, the procedure to estimate Rt was repeated for each Survey (1-4) with a reduction of 20, 35, 50, 65, and 80% of contacts from the POLYMOD UK study  for the 5–17 year age group.
All data were analysed using RStudio Version 1.2.5033 . The code is based on the SocialMixr package  as well as on the work of Jarvis et al. . Funding to support data collection was provided by the Public Health Agency of Canada (PHAC), The National Collaborating Centre for Infectious Diseases (NCCID), and the University of Guelph. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.