A methodology for estimating SARS-CoV-2 importation risk by air travel into Canada between July and November 2021 | BMC Public Health
The model operates at a daily time step to estimate the weekly number of air travellers arriving infected with SARS-CoV-2 at the airport-level from July to November 2021. The model was adapted from a mathematical model previously used to estimate importation risk of dengue and COVID-19 [2, 18]. The key model adaptations adjusted for underreporting in COVID-19 case counts, accounted for the impacts of vaccination and pre-departure testing for SARS-CoV-2 to reduce importation risk, and stratified importation risk by SARS-CoV-2 variants of concern (VOC) and variants of interest (VOI).
Air travel volume data
Model input for air travel volumes was derived from two data sources. Daily travel volumes from each country of departure (i.e. the country from which travel to Canada was initiated) to Canada were derived using Canada Border Services Agency’s (CBSA) Advanced Passenger Information in combination with the overall passage data from CBSA (Additional File 1). Monthly travel volumes for each itinerary from the origin airport to the final Canadian destination airport were obtained from the International Air Transport Authority (IATA) [21]. Finally, the CBSA travel volumes were distributed in proportion to the IATA travel volumes to derive model input at the daily and airport levels.
Traveller groups
In the model, travellers were stratified as essential or non-essential based on their reason for travel. Non-essential travellers, which included those who travelled for personal reasons (e.g. tourism, education), were assumed to have a negative pre-departure molecular test result three days prior to their scheduled departure [11], while essential travellers were exempt from that requirement. Between November 2020 and October 2022, non-essential travellers were required to submit COVID-19 related information [22, 23] via the Government of Canada’s (GoC) digital ArriveCan platform at each entry into Canada. This data source, in combination with the CBSA ContactTrace program, were used to derive the weekly country-specific proportions of non-essential travellers in the model ([24]; Additional file 1).
Travellers were also characterized as being Canadian or foreign residents to distinguish their place of residence as being in Canada or another country, respectively. In the model, Canadian residents were assumed to have spent all their time in Canada, except for the period in which they travelled to a non-Canadian country where they could become infected with COVID-19 and then import the infection into Canada. This time spent outside of Canada was assumed to follow a normal distribution with a mean of 15 days and a standard deviation of 2 days according to recent estimates [25]. Foreign residents were assumed to reside and spend their time only in the country of departure before travel to Canada. This was the country in which they could be infected with SARS-CoV-2 prior to entering Canada. Model input for the country-specific weekly proportions of Canadian and foreign residents were derived from CBSA’s Advanced Passenger Information data (for essential travellers) and ArriveCan and ContactTrace data (for non-essential travellers, Additional file 1).
Finally, travellers were stratified by vaccination status to account for any vaccine-induced immunity. For non-essential travellers, the weekly country-specific distributions of vaccine statuses were derived from the ArriveCan and ContactTrace data and could be one of: unvaccinated, partially vaccinated with a GoC approved vaccine, partially vaccinated with a non-GoC approved vaccine, fully vaccinated with GoC approved vaccines, fully vaccinated with non-GoC approved vaccines or fully vaccinated with a mixture of GoC approved and non-GoC approved vaccines. Hereafter, partially vaccinated refers to vaccination with one dose of a two dose vaccine regime while fully vaccinated refers to one dose of a one dose vaccine regime or two doses of a two dose vaccine regime. The vaccination status of essential travellers was not available from the ArriveCan data because these travellers were not required to provide proof of vaccination during the study period. Model input for the daily distributions of vaccination statuses in essential travellers were assumed to follow the vaccine coverage for the country of departure (foreign resident travellers) or for Canada (Canadian resident travellers) as reported by Our World in Data (OWD; [5]). Vaccination status for essential travellers in the model included only unvaccinated, partially vaccinated or fully vaccinated because OWD did not provide information on vaccine type for us to distinguish between GoC approved or otherwise.
Correcting for underreporting of COVID-19 cases
Reported COVID-19 case data were likely underestimated due to asymptomatic transmission, incomplete testing and imperfect test sensitivity and reporting systems [26]. We derived country-specific correction factors to inflate case data and better reflect the true prevalence (Additional File 1). A semi-Bayesian probabilistic bias approach was used to estimate the number of true cases at the country level, using reported case data and testing rates [27]. We adapted the method to also account for the evolving population-level immunity due to previous COVID-19 infections and increasing vaccination rates. True case counts were estimated from March to August 2020 and then monthly thereafter to reduce instability in estimates caused by sparse case data at the onset of the pandemic and low testing rates [27]. The estimated true case count was divided by the reported case count [5, 28, 29] in order to obtain country-specific correction factors for each time period from March 2020 onwards. Finally, a regression modelling approach was implemented using the country-level Gross National Income (GNI) as a predictor [30] and the calculated correction factor as the dependent variable. This regression model was used to impute the missing correction factors for countries that did not have case, testing, or vaccination data. The GNI was used as a proxy for the effectiveness of the country surveillance system to detect, test and report COVID-19 cases [30].
Model formulation
The probability of a traveller arriving in Canada infected with SARS-CoV-2 accounts for the vaccination status of the traveller and potential immunity acquired from a previous infection in their country of residence (cr). For simplicity, it was assumed that infection- and vaccine-induced immunity did not wane from the beginning of the pandemic until the end of the study period, and prior infections provided complete immunity against re-infection. The probability of a traveller having infection-acquired immunity on any given day d and in country of residence cr \(({Pinf}_{cr,d})\) was calculated as the cumulating proportion of residents reported to have had COVID-19 given the 2020 country population size [5, 31, 32]. For an essential traveller, the probability of vaccine-acquired protection \((Pvac{c\_E}_{cr,d})\) on any given day d and in country of residence cr, was equal to:
$$Pvac{c\_E}_{cr,d}={\sum }_{status} Pro{p}_{cr,d, status}\times {VE}_{cr,status}$$
(1)
where \({VE}_{cr,status}\), vaccine effectiveness, is the probability that a traveller had complete immunity against infection which varied according to COVID-19 vaccination status (partially or fully vaccinated) and the cr for the assumed type of vaccine (mRNA vaccines or others) (Additional file 1: Table A2); and \(Pro{p}_{cr,d, status}\) represents the proportion of the population in country \(cr\) for each vaccination status on day d. Since vaccination status information was available for non-essential travellers, their probability of vaccine-acquired protection \((Pvac{c\_NE}_{cr,status})\) was equal to the associated vaccine effectiveness \({VE}_{cr,status}\).
The probability of a traveller arriving in Canada infected with SARS-CoV-2 depended on their risk of exposure in the country of departure, cd, prior to departure for Canada. The daily probability of infection \(({\beta }_{cd,d})\) for a susceptible person on a given day d in country cd was calculated as the number of new cases (corrected for underreporting) out of the total susceptible population (i.e. the proportion of the population that was not immune to infection with COVID-19 due to prior infection or vaccination). Based on this daily probability of infection, the probability of a traveller arriving in Canada infected with SARS-CoV-2 was calculated according to the traveller’s reason for travel (i.e. essential or non-essential). For an essential traveller, the probability of importation, (\({P\_E}_{s,cd,cr};\) Eq. 2 and Additional file 1), on travel day s was based on the traveller’s probability of acquiring infection on any of the n days prior to departure to Canada, given that they did not have infection-acquired protection \(\left(1-{Pinf}_{cr,d}\right)\) or vaccine-acquired protection \(\left(1-{Pvacc\_E}_{cr,d}\right)\). Here n represents the sum of the latent and infectious periods for SARS-CoV-2 infections (Table 1). The probability of importation for a non-essential traveller, (\({P\_NE}_{s,cd,cr, status}\); Eq. 3 and Additional file 1), was based on the traveller’s probability of acquiring infection on any of the (n –\(\mu\)) days prior to the test day and receiving a false negative test result on test day, or not being infected on test day and acquiring infection after completing the test prior to departure. Here \(\mu\) represents the number of days between the test and travel days (i.e. set at three days in the model). An estimated molecular test sensitivity (se) of 60% was implemented, which represented the mean value when accounting for the variation in sensitivity with respect to time since infection ([33, 34]; Additional file 1). Similar to essential travellers, the probability of importation for non-essential travellers is conditional on not having infection-acquired protection \(\left(1-{Pinf}_{cr,d}\right)\) or vaccine-acquired protection \(\left(1-{Pvacc\_NE}_{cr,status}\right)\).
$${P\_E}_{s,cd,cr}=\left[x -\prod_{d={s-i} }^{s-1}\left(1-{\beta }_{cd,d}\right)\right]\left(1-{Pinf}_{cr,s-\left(i+1\right)}\right)\left(1-{Pvacc\_E}_{cr, s-\left(i+1\right)}\right)$$
(2)
$${P\_NE}_{s,cd,cr, status}=\left[\left(1-se\right)x+se\prod_{d={s-i} }^{s-\left(\mu +1\right)}\left(1-{\beta }_{cd,d}\right)-\prod_{d={s-i} }^{s-1}\left(1-{\beta }_{cd,d}\right)\right]\left(1-{Pinf}_{cr,s-\left(i+1\right)}\right)\left(1-{Pvacc\_NE}_{cr,status}\right)$$
(3)
where
$$i=\left\{\begin{array}{c}t_c,\;when\;traveller\;is\;a\;Canadian\;resident\\n,\;when\;traveller\;is\;aforeign\;resident\end{array}\right.$$
$$x=\left\{\begin{array}{c}\prod_{d=s-t_c}^{s-(n+1)}(1-\beta_{cd,d}),\;when\;traveller\;is\;a\;Canadian\;resident\;and\;t_c>n\\1,\;when\;traveller\;is\;a\;Canadian\;resident\;and\;t_c\leq\;n\;or\;a\;foreign\;traveller\end{array}\right.$$
where \({t}_{c}\) is the number of days spent in the country of departure \(cd\) prior to leaving for Canada. For foreign residents, it was assumed that \({{\text{t}}}_{{\text{c}}}>{\text{n}}\).
Finally, the total number of importations (\({I}_{w}\)) for every epi-week, w, was calculated using the probability of air travellers arriving infected (\({P}_{k,\upgamma ,s}\)) for each airport-level origin–destination travel route (k), each travel group (γ, i.e. Canadian or foreign resident, vaccination status, essential or non-essential traveller) and each day of the week (\(s\)), and the corresponding travel volume (\({v}_{k,\upgamma ,s}\)):
$${I}_{w}=\sum_{k,\upgamma ,\mathrm{ s} }\left[{P}_{k,\upgamma ,s}\times {v}_{k,\upgamma ,s}\right]$$
(4)
Importation estimates were stratified by VOCs and VOIs listed by the USA Centers for Disease Control and Prevention. It was assumed that the proportion of variants reported in the GISAID database [39] for each country during a three-week period (including the week modelled and the two prior weeks) was the same proportion that would be observed in infected travellers arriving in Canada from these countries.
Modelling importation risk and counterfactual scenarios
We used the model to estimate importation risk from July 11 to November 27, 2021 under the assumption that all non-essential travellers were required to have a negative molecular pre-departure test result three days prior to departure for Canada. As well as being our most probable estimate of the true importation risk given the testing requirements that were in effect during the modelled time period, these model estimates formed our baseline to compare with two counterfactual scenarios. Model output is presented by country of departure, SARS-CoV-2 variant and traveller groups. In addition, the number of infected travellers arriving at each of Canada’s four largest airports (Toronto Pearson, Montréal-Trudeau, Vancouver International, and Calgary International) as their final destination are presented. Finally, we mapped country-level model outputs in terms of the cumulative number of importations, percent positivity, and travel volumes for the total study period using ArcGIS Pro version 2.9.0 (ESRI, Redlands, CA).
Two counterfactual scenarios were simulated from July 11 to November 27, 2021 to measure the impact of pre-departure testing on non-essential travellers to reduce importation risk as compared to the baseline. For counterfactual scenario 1, fully vaccinated (with or without GoC approved vaccines) non-essential travellers were not tested, and for counterfactual scenario 2 there was no testing of any non-essential travellers. For both counterfactual scenarios, the model was run for all non-essential travellers, whereas outputs from the baseline scenario were used for essential travellers. The weekly percent change in the total number of imported cases for each counterfactual scenario was compared to the baseline scenario.
Model stochasticity was implemented through the distributions of parameter input values for vaccine effectiveness, latent and infectious periods, and for Canadian travellers, travel duration. For each of these parameters, a value was randomly chosen from a pre-defined distribution (Table 1) for every category of traveller, with these categories consisting of unique combinations of origin–destination airport pathway, essential status and day. The baseline and counterfactual scenarios were simulated 50 times. We only present the mean results because the confidence intervals were too narrow to visualise in the plots. All model simulations and analyses were conducted in R version 4.1.0 [40].
