A methodology for estimating SARS-CoV-2 importation risk by air travel into Canada between July and November 2021 | BMC Public Health

The mannequin operates at a each day time step to estimate the weekly variety of air travellers arriving contaminated with SARS-CoV-2 on the airport-level from July to November 2021. The mannequin was tailored from a mathematical mannequin beforehand used to estimate importation threat of dengue and COVID-19 [2, 18]. The important thing mannequin diversifications adjusted for underreporting in COVID-19 case counts, accounted for the impacts of vaccination and pre-departure testing for SARS-CoV-2 to cut back importation threat, and stratified importation threat by SARS-CoV-2 variants of concern (VOC) and variants of curiosity (VOI).

Air journey quantity information

Mannequin enter for air journey volumes was derived from two information sources. Every day journey volumes from every nation of departure (i.e. the nation from which journey to Canada was initiated) to Canada had been derived utilizing Canada Border Companies Company’s (CBSA) Superior Passenger Info together with the general passage information from CBSA (Extra File 1). Month-to-month journey volumes for every itinerary from the origin airport to the ultimate Canadian vacation spot airport had been obtained from the Worldwide Air Transport Authority (IATA) [21]. Lastly, the CBSA journey volumes had been distributed in proportion to the IATA journey volumes to derive mannequin enter on the each day and airport ranges.

Traveller teams

Within the mannequin, travellers had been stratified as important or non-essential primarily based on their purpose for journey. Non-essential travellers, which included those that travelled for private causes (e.g. tourism, training), had been assumed to have a unfavourable pre-departure molecular take a look at end result three days previous to their scheduled departure [11], whereas important travellers had been exempt from that requirement. Between November 2020 and October 2022, non-essential travellers had been required to submit COVID-19 associated data [22, 23] through the Authorities of Canada’s (GoC) digital ArriveCan platform at every entry into Canada. This information supply, together with the CBSA ContactTrace program, had been used to derive the weekly country-specific proportions of non-essential travellers within the mannequin ([24]; Extra file 1).

Travellers had been additionally characterised as being Canadian or overseas residents to differentiate their place of residence as being in Canada or one other nation, respectively. Within the mannequin, Canadian residents had been assumed to have spent all their time in Canada, aside from the interval by which they travelled to a non-Canadian nation the place they might turn out to be contaminated with COVID-19 after which import the an infection into Canada. This time spent exterior of Canada was assumed to comply with a traditional distribution with a imply of 15 days and a typical deviation of two days in response to latest estimates [25]. Overseas residents had been assumed to reside and spend their time solely within the nation of departure earlier than journey to Canada. This was the nation by which they might be contaminated with SARS-CoV-2 previous to getting into Canada. Mannequin enter for the country-specific weekly proportions of Canadian and overseas residents had been derived from CBSA’s Superior Passenger Info information (for important travellers) and ArriveCan and ContactTrace information (for non-essential travellers, Extra file 1).

Lastly, travellers had been stratified by vaccination standing to account for any vaccine-induced immunity. For non-essential travellers, the weekly country-specific distributions of vaccine statuses had been derived from the ArriveCan and ContactTrace information and might be one among: unvaccinated, partially vaccinated with a GoC authorised vaccine, partially vaccinated with a non-GoC authorised vaccine, totally vaccinated with GoC authorised vaccines, totally vaccinated with non-GoC authorised vaccines or totally vaccinated with a mix of GoC authorised and non-GoC authorised vaccines. Hereafter, partially vaccinated refers to vaccination with one dose of a two dose vaccine regime whereas totally vaccinated refers to at least one dose of a one dose vaccine regime or two doses of a two dose vaccine regime. The vaccination standing of important travellers was not out there from the ArriveCan information as a result of these travellers weren’t required to offer proof of vaccination throughout the examine interval. Mannequin enter for the each day distributions of vaccination statuses in important travellers had been assumed to comply with the vaccine protection for the nation of departure (overseas resident travellers) or for Canada (Canadian resident travellers) as reported by Our World in Knowledge (OWD; [5]). Vaccination standing for important travellers within the mannequin included solely unvaccinated, partially vaccinated or totally vaccinated as a result of OWD didn’t present data on vaccine kind for us to differentiate between GoC authorised or in any other case.

Correcting for underreporting of COVID-19 instances

Reported COVID-19 case information had been probably underestimated because of asymptomatic transmission, incomplete testing and imperfect take a look at sensitivity and reporting methods [26]. We derived country-specific correction elements to inflate case information and higher replicate the true prevalence (Extra File 1). A semi-Bayesian probabilistic bias strategy was used to estimate the variety of true instances on the nation stage, utilizing reported case information and testing charges [27]. We tailored the tactic to additionally account for the evolving population-level immunity because of earlier COVID-19 infections and rising vaccination charges. True case counts had been estimated from March to August 2020 after which month-to-month thereafter to cut back instability in estimates brought on by sparse case information on the onset of the pandemic and low testing charges [27]. The estimated true case rely was divided by the reported case rely [5, 28, 29] with a purpose to get hold of country-specific correction elements for every time interval from March 2020 onwards. Lastly, a regression modelling strategy was applied utilizing the country-level Gross Nationwide Earnings (GNI) as a predictor [30] and the calculated correction issue because the dependent variable. This regression mannequin was used to impute the lacking correction elements for international locations that didn’t have case, testing, or vaccination information. The GNI was used as a proxy for the effectiveness of the nation surveillance system to detect, take a look at and report COVID-19 instances [30].

Mannequin formulation

The likelihood of a traveller arriving in Canada contaminated with SARS-CoV-2 accounts for the vaccination standing of the traveller and potential immunity acquired from a earlier an infection of their nation of residence (cr). For simplicity, it was assumed that infection- and vaccine-induced immunity didn’t wane from the start of the pandemic till the top of the examine interval, and prior infections offered full immunity in opposition to re-infection. The likelihood of a traveller having infection-acquired immunity on any given day d and in nation of residence cr ((Pinf_cr,d)) was calculated because the cumulating proportion of residents reported to have had COVID-19 given the 2020 nation inhabitants measurement [5, 31, 32]. For a vital traveller, the likelihood of vaccine-acquired safety ((Pvacc_E_cr,d)) on any given day d and in nation of residence cr, was equal to:

$$Pvacc_E_cr,d=sum _status Prop_cr,d, statustimes VE_cr,standing$$


the place (VE_cr,standing), vaccine effectiveness, is the likelihood {that a} traveller had full immunity in opposition to an infection which different in response to COVID-19 vaccination standing (partially or totally vaccinated) and the cr for the assumed kind of vaccine (mRNA vaccines or others) (Extra file 1: Desk A2); and (Prop_cr,d, standing) represents the proportion of the inhabitants in nation (cr) for every vaccination standing on day d. Since vaccination standing data was out there for non-essential travellers, their likelihood of vaccine-acquired safety ((Pvacc_NE_cr,standing)) was equal to the related vaccine effectiveness (VE_cr,standing).

The likelihood of a traveller arriving in Canada contaminated with SARS-CoV-2 relied on their threat of publicity within the nation of departure, cd, previous to departure for Canada. The each day likelihood of an infection ((beta _cd,d)) for a vulnerable individual on a given day d in nation cd was calculated because the variety of new instances (corrected for underreporting) out of the full vulnerable inhabitants (i.e. the proportion of the inhabitants that was not resistant to an infection with COVID-19 because of prior an infection or vaccination). Primarily based on this each day likelihood of an infection, the likelihood of a traveller arriving in Canada contaminated with SARS-CoV-2 was calculated in response to the traveller’s purpose for journey (i.e. important or non-essential). For a vital traveller, the likelihood of importation, ((P_E_s,cd,cr;) Eq. 2 and Extra file 1), on journey day s was primarily based on the traveller’s likelihood of buying an infection on any of the n days previous to departure to Canada, provided that they didn’t have infection-acquired safety (left(1-Pinf_cr,dright)) or vaccine-acquired safety (left(1-Pvacc_E_cr,dright)). Right here n represents the sum of the latent and infectious intervals for SARS-CoV-2 infections (Desk 1). The likelihood of importation for a non-essential traveller, ((P_NE_s,cd,cr, standing); Eq. 3 and Extra file 1), was primarily based on the traveller’s likelihood of buying an infection on any of the (n –(mu)) days previous to the take a look at day and receiving a false unfavourable take a look at end result on take a look at day, or not being contaminated on take a look at day and buying an infection after finishing the take a look at previous to departure. Right here (mu) represents the variety of days between the take a look at and journey days (i.e. set at three days within the mannequin). An estimated molecular take a look at sensitivity (se) of 60% was applied, which represented the imply worth when accounting for the variation in sensitivity with respect to time since an infection ([33, 34]; Extra file 1). Much like important travellers, the likelihood of importation for non-essential travellers is conditional on not having infection-acquired safety (left(1-Pinf_cr,dright)) or vaccine-acquired safety (left(1-Pvacc_NE_cr,statusright)).

$$P_E_s,cd,cr=left[x -prod_d=s-i ^s-1left(1-beta _cd,dright)right]left(1-Pinf_cr,s-left(i+1right)proper)left(1-Pvacc_E_cr, s-left(i+1right)proper)$$


$$P_NE_s,cd,cr, standing=left[left(1-seright)x+seprod_d=s-i ^s-left(mu +1right)left(1-beta _cd,dright)-prod_d=s-i ^s-1left(1-beta _cd,dright)right]left(1-Pinf_cr,s-left(i+1right)proper)left(1-Pvacc_NE_cr,statusright)$$


the place



the place (t_c) is the variety of days spent within the nation of departure (cd) previous to leaving for Canada. For overseas residents, it was assumed that (textt_textc>textn).

Desk 1 Parameter values utilized in a COVID-19 importation threat mannequin to Canada

Lastly, the full variety of importations ((I_w)) for each epi-week, w, was calculated utilizing the likelihood of air travellers arriving contaminated ((P_k,upgamma ,s)) for every airport-level origin–vacation spot journey route (okay), every journey group (γ, i.e. Canadian or overseas resident, vaccination standing, important or non-essential traveller) and every day of the week ((s)), and the corresponding journey quantity ((v_k,upgamma ,s)):

$$I_w=sum_k,upgamma ,mathrm s left[P_k,upgamma ,stimes v_k,upgamma ,sright]$$


Importation estimates had been stratified by VOCs and VOIs listed by the USA Facilities for Illness Management and Prevention. It was assumed that the proportion of variants reported within the GISAID database [39] for every nation throughout a three-week interval (together with the week modelled and the 2 prior weeks) was the identical proportion that might be noticed in contaminated travellers arriving in Canada from these international locations.

Modelling importation threat and counterfactual situations

We used the mannequin to estimate importation threat from July 11 to November 27, 2021 underneath the belief that each one non-essential travellers had been required to have a unfavourable molecular pre-departure take a look at end result three days previous to departure for Canada. In addition to being our most possible estimate of the true importation threat given the testing necessities that had been in impact throughout the modelled time interval, these mannequin estimates fashioned our baseline to check with two counterfactual situations. Mannequin output is offered by nation of departure, SARS-CoV-2 variant and traveller teams. As well as, the variety of contaminated travellers arriving at every of Canada’s 4 largest airports (Toronto Pearson, Montréal-Trudeau, Vancouver Worldwide, and Calgary Worldwide) as their remaining vacation spot are offered. Lastly, we mapped country-level mannequin outputs when it comes to the cumulative variety of importations, p.c positivity, and journey volumes for the full examine interval utilizing ArcGIS Professional model 2.9.0 (ESRI, Redlands, CA).

Two counterfactual situations had been simulated from July 11 to November 27, 2021 to measure the influence of pre-departure testing on non-essential travellers to cut back importation threat as in comparison with the baseline. For counterfactual state of affairs 1, totally vaccinated (with or with out GoC authorised vaccines) non-essential travellers weren’t examined, and for counterfactual state of affairs 2 there was no testing of any non-essential travellers. For each counterfactual situations, the mannequin was run for all non-essential travellers, whereas outputs from the baseline state of affairs had been used for important travellers. The weekly p.c change within the whole variety of imported instances for every counterfactual state of affairs was in comparison with the baseline state of affairs.

Mannequin stochasticity was applied via the distributions of parameter enter values for vaccine effectiveness, latent and infectious intervals, and for Canadian travellers, journey length. For every of those parameters, a price was randomly chosen from a pre-defined distribution (Desk 1) for each class of traveller, with these classes consisting of distinctive mixtures of origin–vacation spot airport pathway, important standing and day. The baseline and counterfactual situations had been simulated 50 occasions. We solely current the imply outcomes as a result of the boldness intervals had been too slender to visualise within the plots. All mannequin simulations and analyses had been performed in R model 4.1.0 [40].

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