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Time travel could be possible, but only with parallel timelines

Assistant Professor, Physics, Brock University

Disclosure statement

Barak Shoshany does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Brock University provides funding as a member of The Conversation CA-FR.

Brock University provides funding as a member of The Conversation CA.

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Have you ever made a mistake that you wish you could undo? Correcting past mistakes is one of the reasons we find the concept of time travel so fascinating. As often portrayed in science fiction, with a time machine, nothing is permanent anymore — you can always go back and change it. But is time travel really possible in our universe , or is it just science fiction?

Read more: Curious Kids: is time travel possible for humans?

Our modern understanding of time and causality comes from general relativity . Theoretical physicist Albert Einstein’s theory combines space and time into a single entity — “spacetime” — and provides a remarkably intricate explanation of how they both work, at a level unmatched by any other established theory. This theory has existed for more than 100 years, and has been experimentally verified to extremely high precision, so physicists are fairly certain it provides an accurate description of the causal structure of our universe.

For decades, physicists have been trying to use general relativity to figure out if time travel is possible . It turns out that you can write down equations that describe time travel and are fully compatible and consistent with relativity. But physics is not mathematics, and equations are meaningless if they do not correspond to anything in reality.

Arguments against time travel

There are two main issues which make us think these equations may be unrealistic. The first issue is a practical one: building a time machine seems to require exotic matter , which is matter with negative energy. All the matter we see in our daily lives has positive energy — matter with negative energy is not something you can just find lying around. From quantum mechanics, we know that such matter can theoretically be created, but in too small quantities and for too short times .

However, there is no proof that it is impossible to create exotic matter in sufficient quantities. Furthermore, other equations may be discovered that allow time travel without requiring exotic matter. Therefore, this issue may just be a limitation of our current technology or understanding of quantum mechanics.

The other main issue is less practical, but more significant: it is the observation that time travel seems to contradict logic, in the form of time travel paradoxes . There are several types of such paradoxes, but the most problematic are consistency paradoxes .

A popular trope in science fiction, consistency paradoxes happen whenever there is a certain event that leads to changing the past, but the change itself prevents this event from happening in the first place.

For example, consider a scenario where I enter my time machine, use it to go back in time five minutes, and destroy the machine as soon as I get to the past. Now that I destroyed the time machine, it would be impossible for me to use it five minutes later.

But if I cannot use the time machine, then I cannot go back in time and destroy it. Therefore, it is not destroyed, so I can go back in time and destroy it. In other words, the time machine is destroyed if and only if it is not destroyed. Since it cannot be both destroyed and not destroyed simultaneously, this scenario is inconsistent and paradoxical.

Eliminating the paradoxes

There’s a common misconception in science fiction that paradoxes can be “created.” Time travellers are usually warned not to make significant changes to the past and to avoid meeting their past selves for this exact reason. Examples of this may be found in many time travel movies, such as the Back to the Future trilogy.

But in physics, a paradox is not an event that can actually happen — it is a purely theoretical concept that points towards an inconsistency in the theory itself. In other words, consistency paradoxes don’t merely imply time travel is a dangerous endeavour, they imply it simply cannot be possible.

This was one of the motivations for theoretical physicist Stephen Hawking to formulate his chronology protection conjecture , which states that time travel should be impossible. However, this conjecture so far remains unproven. Furthermore, the universe would be a much more interesting place if instead of eliminating time travel due to paradoxes, we could just eliminate the paradoxes themselves.

One attempt at resolving time travel paradoxes is theoretical physicist Igor Dmitriyevich Novikov’s self-consistency conjecture , which essentially states that you can travel to the past, but you cannot change it.

According to Novikov, if I tried to destroy my time machine five minutes in the past, I would find that it is impossible to do so. The laws of physics would somehow conspire to preserve consistency.

Introducing multiple histories

But what’s the point of going back in time if you cannot change the past? My recent work, together with my students Jacob Hauser and Jared Wogan, shows that there are time travel paradoxes that Novikov’s conjecture cannot resolve. This takes us back to square one, since if even just one paradox cannot be eliminated, time travel remains logically impossible.

So, is this the final nail in the coffin of time travel? Not quite. We showed that allowing for multiple histories (or in more familiar terms, parallel timelines) can resolve the paradoxes that Novikov’s conjecture cannot. In fact, it can resolve any paradox you throw at it.

The idea is very simple. When I exit the time machine, I exit into a different timeline. In that timeline, I can do whatever I want, including destroying the time machine, without changing anything in the original timeline I came from. Since I cannot destroy the time machine in the original timeline, which is the one I actually used to travel back in time, there is no paradox.

After working on time travel paradoxes for the last three years , I have become increasingly convinced that time travel could be possible, but only if our universe can allow multiple histories to coexist. So, can it?

Quantum mechanics certainly seems to imply so, at least if you subscribe to Everett’s “many-worlds” interpretation , where one history can “split” into multiple histories, one for each possible measurement outcome – for example, whether Schrödinger’s cat is alive or dead, or whether or not I arrived in the past.

But these are just speculations. My students and I are currently working on finding a concrete theory of time travel with multiple histories that is fully compatible with general relativity. Of course, even if we manage to find such a theory, this would not be sufficient to prove that time travel is possible, but it would at least mean that time travel is not ruled out by consistency paradoxes.

Time travel and parallel timelines almost always go hand-in-hand in science fiction, but now we have proof that they must go hand-in-hand in real science as well. General relativity and quantum mechanics tell us that time travel might be possible, but if it is, then multiple histories must also be possible.

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Time traveller from the year 2671 confirms four big events happening in December

Eno Alric has named four dates in December when notable events could occur in an effort to prove he is who he says he is.

• 15:03, 20 NOV 2022

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An infamous 'time traveller' from 2671 has "very big things" will happen in December - that will prove their authenticity.

Eno Alric has named the four significant dates in December when notable events could occur in an effort to prove he is who he says he is.

The TikToker - known as 'theradianttimetraveler' - has posted a series of bizarre videos forecasting the future, reports the Daily Mirror.

READ MORE - Dad told to 'get a grip' after 'unreasonable' request to his wife at weekends

Earlier this year he also said he could transport eight people with him to his time within six months.

His latest upload is captioned: "Yes, I am a real time traveller, remember these 4 dates in December 2022."

The 20-second video features foreboding music and pinpoints December 8, 12 and 25 as dates something will happen, while December 20 is "The Release".

Eno added: "Very big things will happen on each of these dates, this will 100% prove that I am a real time traveller."

He gave no indication as to what his viewers should prepare for, but repeated his warning from other recent videos: "Stay safe."

His predictions were met with expected scepticism from commenters, with many teasing him over his failed predictions from last month.

One said: "Yeah right, I still remember the four dates to remember in November. Lol."

Another added: "You said 10 people will receive super power on November 14 2022 that didn’t happen."

A third said: "Guys I'm a time traveler [from] the future. Remember the date December 25th it's a thing called Christmas."

Eno had said this month humans would discover new planets, be struck by a tidal wave and be visited by aliens.

He has 110,000 followers and has promised to reveal his identity once he reaches a million.

His bio says: "From the year 2671, mankind is on the brink of destruction... Face Reveal at 1M."

Eno is not the only TikToker claiming to be a time traveller.

'Time Traveller 3000' claims he predicted Elon Musk would takeover Twitter.

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In a video shared with their 12,000 followers, they said: "To prove that I am a time traveller I will tell you what happens to Elon Musk.

"As I predicted months ago, Elon would buy Twitter and then unban Donald Trump.015'

"This will upset many people so Elon will step down as CEO of Tesla and then become CEO of Twitter."

Another similar trend currently on social media sees people unearth photos from the past, which appear to show people using modern technology, and thus proving they have quantum leaped.

As reported earlier this month, newsreel footage from 1937 appeared to show a woman taking a call on a mobile phone.

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TikTok ‘Time Traveller’ Reveals Five Upcoming Dates To Be Prepared For

The first of these cataclysmic events is due next month.

A TikTok 'time traveller' said to be sent back from the future has informed us of five important dates to put in our calendars. To see the dates, watch video below:

The self-proclaimed 'Time Traveller', @aesthetictimewarper , captioned the TikTok video: "Amazing things to come..."

With over 500,000 likes and 15,000 comments, the post has gained some momentum.

The footage shown is of a time lapse with, what appears to be, a skyline overlooking a city. On top of that are subtitles in which the TikToker makes his bold claims.

Firstly @aesthetictimewarper says: "Many of you still don't believe I am a real time traveler, so remember these five dates."

Shortly after that, a first date and event are given (in US format so month/date/year): "8/3/21: Nasa finds a mirrored Earth, opposite gravity, physics, motion."

We shall look forward to that one, it's supposed to be coming next month.

After comes a more specific event: "9/14/21: A Category 6 hurricane hits South Carolina, the worst in history."

It's not all depressing, as the time traveller's next event could be quite cool.

"10/20/21: 8 humans receive superpowers from extreme energy of the Sun."

Now that I wouldn't mind seeing, of course, as long as they use their powers for good. No Thanoses please.

Next up is one for all you dinosaur fanatics/wannabe Ross Gellers.

"12/14/21: 3 Teenagers find a T-Rex egg and a device to open a portal to an alternate universe."

Lastly, this event is predicted to happen next year and it could be a big one.

"2/2/2022: Atlantis is found in the Atlantic Ocean, housing human-fish life."

As one might imagine, the comments section was full of questions and observations.

One user from South Carolina was very concerned and asked: "Um I am very nervous about to hurricane in SC that is where I am. What part of SC?"

Whilst another 'time traveller' was quick to point something out: "I'm a time traveler too and I don't see you at the meetings."

A third user threatened to take legal action if events were proved to be wrong.

The comment read: "OK 'Mr. time traveler' if that is your real name, I saved this vid and these dates so if this don't happen I'm suing, I want my superpowers!"

The 'time traveller' has over 1.4 million likes and 230,000 followers on TikTok and according to the bio, wants 'to help humanity' and 'there is a lot you need to know'.

Topics:  time travel , TikTok

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In 1964, a group of scientists create a portal that takes them to a barren, mutant inhabited, Earth in the year 2071. In 1964, a group of scientists create a portal that takes them to a barren, mutant inhabited, Earth in the year 2071. In 1964, a group of scientists create a portal that takes them to a barren, mutant inhabited, Earth in the year 2071.

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Reena : Don't you like me?

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The Time Travelers play a large variety of familiar classic rock songs that all have one thing in common…

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Family friendly classic rock for ALL occasions!

The 32 Best TV Shows About Time Travel

Time traveling is a popular topic when it comes to all types of entertainment from books to films. But in recent years time travel has also become a popular theme in TV.

So let’s take a look at this list of the best time traveling TV shows and find out how each of them handles time travel and all the history that comes with it.

Doctor Who, BBC One (1963 – 1989, 2005 – present)

When it comes to time traveling and TV, probably the most notable name in this niche is Doctor Who  because this time travel series has been around for 39 seasons and is still going strong.

Hailing from British television channel BBC One, Doctor Who tells the tale of the Time Lord aka The Doctor, and his companions as they travel to different times and try to prevent evil forces from changing history and hurting innocent lives.

Once the Time Lord gets hurt beyond healing, he can transform into a new body and continue saving the world. Hence why at this point 13 (soon to be 14) different actors have played The Doctor.

Doctor Who is not only a huge part of the fabric of British popular culture but by now this time travel show has found its way into the hearts of many people all over the world.

It has inspired many spin-offs in the form of TV shows, comic books, movies, novels, you name it. But more than that, by now it has become an industry standard both when it comes to science-fiction television series and shows about time travel.

No wonder that Doctor Who continues to be successful after countless actor changes and plot twists.

Where to watch Doctor Who:

Timeless, nbc (2016 – 2018).

Another time travel TV series that has already become a cult classic and is adored by fans all over the world is NBC’s Timeless . And despite the turmoil that this show has gone through, it still is time traveling at its best.

Starring Malcolm Barrett, Matt Lanter, and Abigail Spencer as Rufus, Wyatt, and Lucy, Timeless  details the trio traveling to different times in an effort to stop their adversaries from rewriting history.

But as it later turns out, the conspiracy goes deeper than them just changing history. Since the people who our trio is chasing are traveling through time to take down a dangerous and all-powerful organization. The same one that helped build the time machine that Rufus, Wyatt, and Lucy are using.

And although Timeless went on for just two seasons (and a two-hour wrap-up movie), you should still check out the show because it’s not only entertaining but will make you think and want to know more about the events that each episode is exploring.

Where to watch Timeless:

Dc’s legends of tomorrow, the cw (2016 – present).

If you are a fan of superhero TV shows, then you will probably have heard about DC’s Legends of Tomorrow . It is a show that is a huge part of The CW’s Arrowverse. And has crossed over with shows like Arrow , The Flash , and Supergirl multiple times now.

And even if you don’t like the rest of the superhero series but do enjoy a good old time travel TV show, then I suggest you still give Legends of Tomorrow a watch.

The plot of this show is based around a team of superheroes that are traveling through time in their time machine christened the Waverider to prevent different catastrophes from happening. Both ones made by others and those created by the team’s previous adventures.

At the forefront, there are well-known DC heroes like Rip Hunter, Firestorm, The Atom, Kid Flash, Steel, and Vixen. Joined by some original characters like Caity Lotz’s White Canary among others.

One of the defining characteristics of Legends of Tomorrow is how fun it is. Because adjectives like unapologetic, witty, and entertaining are frequently used to describe this time travel series.

However, more than that, it adds an interesting layer to the whole Arrowverse universe. And above all, it is just a hoot to watch.

Where to watch Legends of Tomorrow:

12 monkeys, syfy (2015 – 2018).

Then there also is SyFy’s 12 Monkeys , which is a little darker take on time traveling. One that comes with mystery, drama, and apocalyptic stakes. But that doesn’t lessen how good this time travel TV series is.

Split between two timelines, 12 Monkeys centers on Aaron Stanford’s James Cole, who is tasked to travel back in time and stop the distribution of a virus that has the ability to end the human race as we know it.

In Cole’s real timeline, the year is 2043 and people are struggling to survive because of the terrible mutations caused by the virus. So Cole travels back to 2015 to find virologist Cassie Railly, played by Amanda Schull, that can help him stop the release of the virus and the organization that is behind it called The Army of the 12 Monkeys.

If you think about it, the post-apocalyptic setting and time travel really do go hand in hand. Because if you can go back in time to stop history from being changed, why not go back to change it if it prevents something terrible from happening?

And that is what this show explores. Beautifully combining elements of mystery, drama, and science fiction, to form a great TV show.

Where to watch 12 Monkeys:

Outlander, starz (2014 – present).

Want another show that mixes time travel with historical events and does it flawlessly? Then you should put Outlander on your must-watch TV show list!

The show starts in the 1940s when a combat nurse Claire Randall visits Inverness, Scotland as part of her second honeymoon with her husband Frank. Claire accidentally happens upon the standing stones at Craigh na Dun which transport her back in time to 1743.

To return to her own time she first has to survive 18th-century Scotland. And she does so by joining a group of rebel Highlanders from Clan MacKenzie and marrying one of the Highlanders, Jamie Fraser. But eventually, she falls in love with her new husband and aids the clan in evading British redcoats that are pursuing them.

Over the five seasons of Outlander that are currently out (with the sixth coming soon), we see Claire jump back and forth between the 20th and 18th centuries and her two families as she faces two pregnancies, wars, and much more. But eventually, Claire finds her way back to Jamie.

Where to watch Outlander:

Travelers, showcase (2016 – 2018).

Then we have Travelers , a joint venture between Netflix and Canada’s Showcase that will tick all of your time travel TV show boxes.

Set in a post-apocalyptic world , this show depicts the adventures of travelers – operatives who go back in time to prevent the collapse of society.

These travelers are transferred into the bodies of our current-day humans, who otherwise would die, to blend in with twenty-first-century people. And with the help of their artificial intelligence boss from the future, travelers carry out missions in order to stop many catastrophic events from happening.

Travelers is a great mix of sci-fi and drama, featuring a great cast and spine-tingling storylines. So if you love all that and love a good time-travel series, then look no further than Travelers .

Where to watch Travelers:

Dark, netflix (2017 – 2020).

Netflix’s first German original series was the science fiction series Dark , which mixes in some mystery drama with sci-fi: time travel, the apocalypse, wormholes, and parallel worlds.

Dark takes place in Winden, a fictional German town, and begins in 2019 after children begin to disappear from the town. As the show progresses, however, timelines jump drastically between as early as 1921 to as late as 2053.

As four families in Winden investigate the disappearances to reunite with their lost loved ones, they discover a wormhole beneath the local powerplant that allows them to travel between timelines, thus uncovering a generations-long conspiracy involving the town and their families.

Where to watch Dark:

The umbrella academy, netflix (2019 – present).

Netflix brings another to the list with The Umbrella Academy .

On October 1, 1989, 43 infants were suddenly born from unsuspecting women despite them not even being pregnant the day before.

7 of them were raised together as the Hargreeve siblings and trained in their respective abilities until their relationship became strained as teenagers and they drifted apart.

Now, as adults, they’re brought back together by the death of their adoptive father – and the threat of the end of the world, of course.

They’re forced to travel back in time but end up in different times and places, and must find each other again to stop the nuclear apocalypse.

Where to watch The Umbrella Academy:

Seven days, upn (1998 – 2001).

We know that the National Security Agency has its share of secrets, but what if one of those secrets was a time-traveling machine?

In UPN’s Seven Days , the plot centers on one such device made from alien technology found at Roswell.

The Chronosphere, as it’s called, can only be used in times when national security is at risk – the limited capacity of the device allows for just one human to go back in time by seven days in order to avert disasters.

Thus, when the White House is attacked, the NSA employs former Navy SEAL and CIA operative Frank Parker to go back and prevent it from happening.

Where to watch Seven Days:

Loki, disney+ (2021 – present).

Yes, the Marvel Cinematic Universe is one of the greatest gifts to the cinema of our time. Now, the MCU has expanded even further into the television medium and we’ve got a few series to accompany it!

One of those is Loki , which of course, centers on the God of Thunder’s mischievous adopted brother.

After the events in Avengers: Endgame , particularly his stealing of the Tesseract, Loki inadvertently creates another timeline that began in 2012, making him a “time variant” version of himself.

When confronted by the authorities, Loki is given two choices: face punishment and cease to exist, or travel through time to fix his own mess and the threat that has emerged.

Where to watch Loki:

Making history, fox (2017).

The thing about traveling back in time is, you have to be very careful that your actions in the past won’t affect the future (which is essentially your actual present).

Most of the time, that’s something you wouldn’t know until you go back to your time. In Making History , however, Dan Chambers travels back in time to right before the American Revolution and sets off a series of events that seriously mess up the future.

Being able to constantly travel between time periods, Dan recruits the help of history professor Chis Parrish to travel with him and ensure that the American Revolution still takes place.

Where to watch Making History:

Quantum leap, nbc (1989 – 1993).

The title of NBC’s sci-fi comedy-drama Quantum Leap is also the name of the time travel machine that accidentally sends its creator, physicist Dr. Sam Beckett, back into the past.

Now, he’s stuck – and not as himself, either!

Sam discovers that he jumped into the body of a stranger and because he’s still himself, doesn’t know all the details of his current identity.

With the help of his friend Al, who appears as a hologram only he can see, he must fix something that went wrong so he can jump in time again and eventually get back to his own body.

Where to watch Quantum Leap:

Quantum leap, nbc (2022 – present).

Speaking of Quantum Leap , in 2022 NBC revived the 1989 series into a more modern take on the cult classic.

In this new Quantum Leap , thirty years have passed since Dr. Sam Beckett vanished into the Quantum Leap accelerator, and the Quantum Leap project was put to rest.

Now the project is restarted with a new team, who tries to puzzle together the mysteries behind Beckett and his time-traveling machine.

So, we follow Ben Song, the lead physicist of the Quantum Leap time travel project, who gets lost in the past after leaping back in time.

As he tries to return to the present he is helped by his fiancée Addison Augustine, who appears to him as a hologram during each leap, and the team back in the present time.

Where to watch Quantum Leap reboot:

The way home, hallmark channel (2023 – present).

Among the newest time travel shows on this list is Hallmark’s The Way Home which has already been renewed for a second season.

The Way Home follows three generations of Landry women who learn that they can time travel after discovering a magic pond on their family’s farm in Port Haven.

When Kat and her daughter Alice return to Port Haven and are forced to move in with Alice’s estranged mother Del, the three women use time travel to uncover their family history, including what really happened to Kat’s little brother Jacob and whether they can prevent his disappearance.

Where to watch The Way Home:

Russian doll, netflix (2019 – 2022).

Netflix’s Russian Doll deviates from the traditional time travel theme of a willing traveler in one specific timeline because Russian Doll’s protagonist Nadia Vulvokov not only has absolutely no choice or control over her so-called time traveling, but hers is also a time loop.

She wakes up every day having to relive the day of her 36th birthday party in New York City; every time, she dies and comes back to the exact same moment.

Every time, Nadia scrambles to figure out what happens to her and tries to prevent her death, leading her to find Alan, a man who is experiencing the same time loop.

Where to watch Russian Doll:

Undone, prime video (2019 – present).

Undone may be an animated series, but it certainly isn’t geared toward younger audiences; though there is a touch of comedy, the series leans more towards the psychological drama genre and “explores the elastic nature of reality”.

The series follows Alma Winograd-Diaz right after she gets into a near-fatal car accident.

Right before the crash, she has a strange vision of her dead father, and right after it, she finds that she now has the ability to manipulate and move through time.

Using this newfound power, she travels between time periods to get to the bottom of the mystery surrounding her father’s death.

Where to watch Undone:

Voyagers, nbc (1982 – 1983).

Premiering back in the early 1980s, NBC’s Voyagers! Is set in a world where time travel already exists.

In fact, there’s already a secret society in place that trains its members, called Voyagers, to go back in time and make sure that historical events happen exactly the way they’re supposed to – otherwise it could affect the present in unexpected ways.

One such Voyager is Phineas Bogg, although he isn’t exactly the best at the job.

During an accidental trip to 1982, he meets the young Jeffrey Jones and ends up bringing him along on one of his missions.

Having lost his Guidebook, Phineas now needs to rely on the extremely smart Jeffrey to get history right.

Where to watch Voyagers!:

Fringe, fox (2008 – 2013).

Fox’s Fringe is a series that was well into the science fiction genre, with parallel universes, supernatural abilities, biotechnology, doomsday predictions, and of course, time travel.

The title is taken from fringe science, which is a branch that deals with scientific theories riddled with skepticism or even having been disproven already.

In Fringe , Special Agent Olivia Dunham is assigned to oversee the FBI ’s Fringe Division, which is run by Peter Bishop and his father Walter.

Together, the team uses both fringe science and Olivia’s knowledge in investigative techniques to explore the unexplained.

In the process, they discover a larger mystery involving parallel universes and alternate timelines .

Where to watch Fringe:

Time after time, abc (2017).

ABC’s Time After Time is based on the novel of the same name written by Kevin Williamson in 1979.

In addition to that, each episode takes its title from a line in Cyndi Lauper’s song, which was inspired by the film (and subsequently, the same book!).

In Time After Time , we are taken to H.G. Wells’ home in 1893.

During a dinner party, he reveals his time machine – right before his guest John Stevenson is arrested for actually being Jack the Ripper .

John escapes through the time machine and Wells follows him straight into the present: 2017. Thus begins a cat-and-mouse game as John attempts to gain control of the machine.

Where to watch Time After Time:

11.22.63, hulu (2016).

When you have anything with Stephen King involved, you know it’s going to be great.

Hulu’s eight-episode miniseries 11.22.63 is based on King’s novel 11/22/63 and is a science fiction thriller like no other.

Starring James Franco in the lead role, 11.22.63 follows Jake Epping, an English teacher from Maine .

His best friend Al reveals a time travel machine and asks him to take over the mission he’s been working on: to travel to the 60s and prevent the assassination of President John F. Kennedy.

Will Jake be successful in changing a past that simply refuses to be changed?

Where to watch 11.22.63:

The 4400, usa network/sky one (2004 – 2007).

The 4400 is yet another slightly different take on the idea of time travel, in that there has been just one (fairly significant) shift forward in time, to the present.

Beginning in 1946, individuals who were easily overlooked or marginalized by society slowly began disappearing through beams of green light.

Now, all 4400 of them (hence the title) have been returned to the present day – without having aged a day and in some cases, even manifesting supernatural abilities like telekinesis, healing, and telepathy.

Tom Baldwin and Diana Skouris are assigned to investigate the phenomenon and find out why the 4400 have returned.

NOTE: For a fresher take on the show, you can also check out the reboot of the original series which is currently airing on The CW.

Where to watch The 4400:

Somewhere between, abc (2017).

When tragedy strikes our lives, we always wish there was something we could’ve done to prevent it.

In ABC’s Somewhere Between we meet Laura Price, a successful news producer with a great career, a loving husband who’s a district attorney, and a beautiful daughter named Serena.

However, her life changes when the serial killer she is helping the cops to catch kills Serena.

Distraught with grief , Laura attempts to complete suicide but is unsuccessful, instead waking up having time-traveled to a week before Serena’s death.

She teams up with Nico, a former SFPD detective who experienced the same reset and wants to find the real killer to change his brother’s fate as well.

Where to watch Somewhere Between:

Terra nova, fox (2011).

Terra Nova takes its viewers to both extremes of the time-traveling timeline.

The present-day is 2149, where overpopulation has threatened to deplete the Earth’s resources.

In an attempt to save Earth and mankind, scientists have found a way to travel back in time, sending groups of humans back to the Cretaceous Period to set up colonies.

Terra Nova focuses primarily on Elisabeth and Jim Shannon, and their three children, who have joined the 10th pilgrimage to Terra Nova.

They offer their expertise as a trauma surgeon and former narcotics detective and help those in charge with stopping those whose intentions go against the greater good.

Where to watch Terra Nova:

Frequency, the cw (2016 – 2017).

One concept in time travel is known as “the butterfly effect”, wherein one small change in time may have great effects elsewhere.

Frequency demonstrates this concept perfectly.

Raimy Sullivan is an NYPD detective who, after a strange weather phenomenon, discovers that she can communicate with her dead father through his old ham radio.

Believing he was a corrupt cop, she learns the truth and warns him of his murder, thus saving his life.

However, this has profound effects on the future – Raimy’s present.

Now, they must work together across time to save her father and preserve the present.

Where to watch Frequency:

Life on mars, bbc one (2006).

In many of the shows on the list so far, the protagonists experience a time loop that’s triggered at the point of their death.

It’s no different for Sam Tyler, the main character in the British series Life on Mars .

Sam is a Detective Chief Inspector with the Greater Manchester Police, but one day he accidentally gets hit by a car.

When he awakens, he’s in 1973 and working at one rank lower than he was: Detective Inspector.

The selling point of Life on Mars , however, is that we’re left unsure if Sam’s predicament is due to his actual death, a comatose, or time travel.

Where to watch Life on Mars:

Always a witch, netflix (2019 – 2020).

Always A Witch (or Siempre Bruja in its original Spanish title) is a Colombian series that is set in both present-day Colombia and the 17th century .

The series follows Carmen Eguiliuz, a young 19-year-old witch who, after committing the crime of falling in love with a white man in 1646 colonial Colombia, is scheduled to be burned at the stake.

She gets a chance to escape to a new life when the mysterious wizard Aldemar makes a deal with her: he will save the man she loves if she travels into the future to find the woman who can break his curse.

Where to watch Always a Witch:

Beforeigners, hbo (2019 – present).

HBO’s Beforeigners is a Norwegian sci-fi crime drama series and the first Norwegian original from HBO Europe.

The title is a clever play on words centered on the general plot: a group of “foreigners” has suddenly shown up at a neighborhood in Oslo, and they are all from “before” times, or several different time periods in history.

Whether from the Viking period , the Stone Age, or the more recent 19th century , each of these ‘Beforeigners’ tries to integrate in modern-day Norwegian society.

One of them even partners with a detective to investigate first a murdered Stone Age woman, then a series of murderers tied to Jack the Ripper.

Where to watch Beforeigners:

Alice, sbs tv (2020).

Alice was a South Korean sci-fi series that aired in late 2020.

In the lead-up to the main plot, the show’s background is explained to its viewers.

Set in 2050, time travel is monitored by an agency called Alice, which sends its clients to the past to help find closure with deceased loved ones.

Alice one day sends two agents to 1992 in order to find the Book of Prophecy, but one of them disappears with the book and her unborn child.

In 2020, the child becomes a detective and in his investigation into his mother’s death in 2010, discovers the existence of Alice and time travel.

Where to watch Alice:

Live up to your name, tvn (2017).

Yet another South Korean time travel series , Live Up to Your Name initially takes its viewers some 400 years into the past, right in the middle of the Joseon dynasty.

There we meet Heo Im, a doctor of traditional Korean medicine who also specializes in acupuncture.

On one of his treatments of the king’s migraines, he made a mistake and was charged with treason.

Chased by the king’s soldiers, he’s shot with an arrow and presumed dead when he falls into the river – except he ends up waking up in present-day Seoul instead, where he meets cardiothoracic surgeon Choi Yeon-kyung.

Where to watch Live Up to Your Name:

My only love song, netflix (2017).

Our third South Korean series is Netflix’s My Only Love Song , which aired in 2017.

We start off in modern-day Korea where we meet Soo-jung, a talented and top-level actress.

However, it seems that the fame may have gotten to her head as she’s arrogant, and believes fame and money make the world go round.

When things don’t go her way on her new show, she winds up in a time-traveling van that takes her to the 6th century.

There, she meets a man much like herself in terms of arrogance, but his hidden soft spot and generosity towards the poor changes her perspective on her own life and self.

Where to watch My Only Love Song:

Signal, tvn (2016).

Signal is based on the 2000 American film Frequency , but another thing that sets this South Korean series apart from others is that the cases investigated in the series are also based on real-life crimes in the country.

Signal follows a cold case profiler from 2015 and a detective from 1989 simultaneously; they discover they’re able to communicate with each other through an old walkie-talkie.

Using this unique ability to provide much-needed foresight in investigations, they team up to both solve and in some cases, even prevent these horrific crimes.

Where to watch Signal:

Rooftop prince, sbs (2012).

Last but not least, South Korea brings its last time-traveling series to the table with Rooftop Prince , a comedy-drama filled with intrigue, mixed identities, and possible reincarnations.

Crown Prince Lee Gak from the Joseon dynasty accidentally time travels to 2012 with three others from his entourage, and their lives are thrown into a whirlwind.

He crosses paths with Se-na, who looks exactly like his recently deceased wife.

In the hopes of getting answers about his wife’s mysterious drowning, he assumes the identity of another man who he also looks exactly like and attempts to marry Se-na in this timeline as well.

Where to watch Rooftop Prince:

11 comments.

Tomorrow people cw

You forgot The Time Tunnel, an Irwin Allen sci-fi show (Voyage to the Bottom of the Sea, Lost In Space, Land of The Giants), all classic 60s sci-fi

Journeyman should also be on this list. It was only half a season on NBC but it wraps up to a satisfying conclusion.

Fantastic acting and interesting characters.

Glad someone else watched Journeyman. I thought I’d was a great spiritual successor to Quantum Leap.

Journeyman is one of the good shows u can watch but qunatum leap i watched and didnt like

Where is The Time Tunnel?????

Another show for your list is “Being Erica” (CBC, 2009-2011). Excellent writing, and very unique.

i was looking for this comment. such an underrated show

I concur. This was definitely a great one. It certainly provides a lot of food for thought.

Some of the information in the Doctor Who one is wrong. It started in 1963, it was only revived in 2005 (you put 2006), and it’s been going for 39 seasons, as of June 2022

Thanks for letting me know! I updated the article accordingly.

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• Open access
• Published: 19 April 2024

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

• Rachael M. Milwid 1 , 6   na1 ,
• Vanessa Gabriele-Rivet 1 , 6   na1 ,
• Nicholas H. Ogden 1 , 3 , 6 ,
• Patricia Turgeon 1 , 3 , 6 ,
• Aamir Fazil 2 ,
• David London 4 ,
• Simon de Montigny 5 &
• Erin E. Rees 1 , 3 , 6  

BMC Public Health volume  24 , Article number:  1088 ( 2024 ) Cite this article

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Metrics details

Estimating rates of disease importation by travellers is a key activity to assess both the risk to a country from an infectious disease emerging elsewhere in the world and the effectiveness of border measures. We describe a model used to estimate the number of travellers infected with SARS-CoV-2 into Canadian airports in 2021, and assess the impact of pre-departure testing requirements on importation risk.

A mathematical model estimated the number of essential and non-essential air travellers infected with SARS-CoV-2, with the latter requiring a negative pre-departure test result. The number of travellers arriving infected (i.e. imported cases) depended on air travel volumes, SARS-CoV-2 exposure risk in the departure country, prior infection or vaccine acquired immunity, and, for non-essential travellers, screening from pre-departure molecular testing. Importation risk was estimated weekly from July to November 2021 as the number of imported cases and percent positivity (PP; i.e. imported cases normalised by travel volume). The impact of pre-departure testing was assessed by comparing three scenarios: baseline (pre-departure testing of all non-essential travellers; most probable importation risk given the pre-departure testing requirements), counterfactual scenario 1 (no pre-departure testing of fully vaccinated non-essential travellers), and counterfactual scenario 2 (no pre-departure testing of non-essential travellers).

In the baseline scenario, weekly imported cases and PP varied over time, ranging from 145 to 539 cases and 0.15 to 0.28%, respectively. Most cases arrived from the USA, Mexico, the United Kingdom, and France. While modelling suggested that essential travellers had a higher weekly PP (0.37 – 0.65%) than non-essential travellers (0.12 – 0.24%), they contributed fewer weekly cases (62 – 154) than non-essential travellers (84 – 398 per week) given their lower travel volume. Pre-departure testing was estimated to reduce imported cases by one third (counterfactual scenario 1) to one half (counterfactual scenario 2).

Conclusions

The model results highlighted the weekly variation in importation by traveller group (e.g., reason for travel and country of departure) and enabled a framework for measuring the impact of pre-departure testing requirements. Quantifying the contributors of importation risk through mathematical simulation can support the design of appropriate public health policy on border measures.

Peer Review reports

Government public health organisations are responsible for assessing the risk of importation of infectious diseases (e.g. [ 1 ]). To be effective, such risk assessments can use modelling methods that integrate data on incoming travel volumes from source endemic/epidemic locations through the global travel network, and country-specific epidemiological and vaccine coverage data [ 2 , 3 ]. In addition to assessing the spatio-temporal risk of importation, models can also be used to quantify the effectiveness of specific prevention strategies prior to their implementation, or post-hoc as a means of on-going evaluation and support for preparedness [ 4 ]. This can be accomplished by comparing estimated importation rates with measures in place against scenarios in which border measures are removed.

SARS‑CoV‑2, the causative agent of COVID-19, spread rapidly across the world resulting in nearly 300 million reported cases and 5.5 million reported deaths by the end of 2021 [ 5 ]. From March 2020 to September 2022, the Canadian government implemented border measures to slow the importation of COVID-19 cases arising from international air travel [ 6 ] (Fig.  1 ). These measures included restrictions on foreign nationals entering Canada [ 6 ], flight suspensions from selected countries [ 7 ], vaccination requirements to enter Canada [ 8 ], pre-departure molecular testing for SARS-CoV-2 within 72 h of departure [ 9 ], quarantine and further testing upon entry into Canada [ 10 , 11 ], and post-entry testing. Some travellers were exempt from some or all of the border measures depending on their reason for travel (e.g. providing an essential service) [ 12 ].

Summary of Canadian border measures implemented and eased in 2020–2021 [ 6 , 13 , 14 , 15 ]. NE = Non-essential

During the COVID-19 pandemic, importation models were used to estimate the number of imported cases from domestic and international travel, and assess the impact of border measures [ 16 , 17 , 18 , 19 ]. In Canada, mathematical models were developed within the first few months of the pandemic to assess the impact of importation on local COVID-19 transmission in specific provinces (e.g. Québec and Ontario [ 19 ], and Newfoundland and Labrador [ 20 ]). At the national-level, an importation modelling method was implemented by the Public Health Agency of Canada’s (PHAC) modelling team to assess possible rates of importation of cases throughout the pandemic, with and without border measures. This study aimed to describe the mathematical model developed by PHAC and estimate the weekly importation risk from air travellers into Canadian airports from July to November 2021 as measured by the number of travellers infected with SARS-CoV-2 (i.e. imported cases) and percent positivity, PP (i.e. imported cases normalised by total travel volume). In addition, the impact of pre-departure testing of non-essential travellers to reduce importation risk was assessed by comparing estimated imported cases against counterfactual scenarios.

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:

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 \(\left(1-{Pvacc\_NE}_{cr,status}\right)\) .

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 ( \({v}_{k,\upgamma ,s}\) ):

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 ].

The importation model estimated that a total of 7,863 infected travellers entered Canada by air from July 11 to November 27, 2021. Most cases originated from the USA (2,890 cases), the country with the highest incoming travel volume to Canada (1.46 million travellers) and a PP of 0.198% (Fig.  2 a, b). Other countries with a high risk of importation were Mexico (1,034 cases; 0.414% PP; 249,462 travellers), the United Kingdom (429 cases; 0.277% PP; 154,715 travellers), and France (335 cases, 0.145% PP; 230,295 travellers) (Fig.  2 ). The relative ranking of contributing countries evolved over time, and differed between destination airports (Figs. 2 and 3 , and Fig. A2 in Additional file 1 ).

Maps illustrating results at the country of departure level from July 11, 2021 to November 27, 2021 for A estimated travel volume to Canada, and model estimates for B COVID-19 percent positivity of travellers entering Canada, and C number of imported COVID-19 cases to Canada. The destination country, Canada, is shown in white. Countries in grey either have unavailable travel volume data and/or reported case counts

Model output for the mean number of SARS-CoV-2 infected air travellers by variant and country of departure arriving at their final destination in one of the four largest Canadian airports, as estimated from July 11 to November 27, 2021

The composition of SARS-CoV-2 variants also varied between airports and through time. Throughout the study period the Delta variant was modelled to be the predominant infectious agent in travellers arriving at the Canadian destination airports. There were also estimated contributions from the Gamma, Mu, and Alpha variants, especially prior to August (Fig.  3 ; Fig. A2 in Additional file 1 ).

Output from the importation model suggests that the number of imported cases and PP also varied over time. There was a peak in August, followed by a decrease until the end of October, and a subsequent increase in November (Fig.  4 ). In the baseline scenario, the mean weekly number of imported cases ranged from 145 to 539 cases and PP ranged from 0.15 to 0.28%. Most cases were imported by non-essential travellers (range: 84–398 per week), who comprised the largest proportion of travel volume (range: 79–90% per week) and populations with full vaccination status (range: 67–92% per week). In contrast, essential travellers had fewer imported cases (range: 62–154 per week), with a smaller travel volume (range: 10–21% per week) and populations of full vaccination status (range: 29–76% per week). Despite having lower importation numbers, the PP in essential travellers was consistently higher (range: 0.37–0.65% per week) than non-essential travellers (range: 0.12–0.24% per week).

Weekly model inputs for the study period (July to November 2021) for A estimated travel volumes into Canada for essential and non-essential travellers, B proportions of fully vaccinated travellers estimated for essential travellers given global vaccine coverage [ 5 ] and reported for non-essential travellers [ 23 ], and model output for C percent positivity and D number of imported COVID-19 cases into Canada as stratified into essential and non-essential travellers and combined (overall) for the baseline scenario (pre-departure testing of all non-essential travellers), counterfactual scenario 1 (no pre-departure testing of fully vaccinated non-essential travellers) and counterfactual scenario 2 (no pre-departure testing of any non-essential travellers). In C ) and D ), the essential traveller curve is identical for all three scenarios since the model for essential travellers was not repeated for the counterfactual scenarios

The counterfactual analysis suggested that pre-departure testing in non-essential travellers reduced importation risk. Compared to the baseline scenario, the risk of importation in non-essential travellers was greater in the counterfactual scenarios, with up to 775 weekly importations (PP ≤ 0.38%) when fully vaccinated travellers were exempt from pre-departure testing (counterfactual scenario 1), and up to 961 weekly imported cases (PP ≤ 0.47%) when all non-essential travellers were exempt from testing (counterfactual 2; Fig.  4 ). Pre-departure testing in the baseline scenario averted 30% of cases occurring over the study period compared to counterfactual scenario 1, with 12 to 36% of cases prevented weekly (Fig.  5 ). Even more cases (43%) were prevented when comparing the baseline scenario to counterfactual scenario 2, with 36 to 45% of cases prevented weekly (Fig.  5 ). The percentage of cases averted in counterfactual scenario 1 increased with time, especially between July and September. For counterfactual scenario 2 the temporal trends on the impact of testing were less pronounced (Fig.  5 ).

Weekly percentage of infected travellers averted from arriving at Canadian airports from July to November 2021 when comparing the baseline scenario (pre-departure testing of all non-essential travellers) to counterfactual scenario 1 (no pre-departure testing of fully vaccinated non-essential travellers) and to counterfactual scenario 2 (no pre-departure testing of any non-essential travellers)

A mathematical model estimating the importation risk of COVID-19 into Canada by combining detailed travel volume data with the evolving global epidemiological landscape and country-specific levels of vaccine- and infection-acquired immunity is presented in this study. The study results suggest that the risk, as measured through the number of travellers arriving infected with SARS-CoV-2 and PP, varied over time by country and Canadian destination airports. Considering the entire study period, the highest overall number of imported COVID-19 cases were estimated to originate from the USA, Mexico, UK, and France. Findings from this study highlight the differential impact of essential and non-essential travellers on COVID-19 importations between July and November 2021. Notably, results from the counterfactual modelling analyses support the effectiveness of pre-departure molecular testing in all non-essential travellers to reduce the number of imported COVID-19 cases.

Flexibility in the model structure and detailed importation risk profiles allow for more nuanced assessments supporting evidence-based policy decision making. By including COVID-19 variant data and detailed travel volumes at the airport level, the model provides a comprehensive characterisation of importation risk by country of departure, variant and point of entry throughout Canada. Furthermore, estimates of importation risk at the airport level allows an evidence-based assessment of the risk and the potential impact on transmission dynamics in the region where the airport is located. In the case of an emergent VOC, the model outputs could be valuable to help target surveillance and on-arrival response efforts towards locations where passengers at higher risk are landing.

Our modelling approach enabled a comprehensive understanding of importation risk through two measures. The PP represents the mean individual-level probability of importation for a given traveller group or country. The number of imported cases provides insight on the level of risk that the traveller group or country poses to Canada by considering the relative importance of both PP and travel volume. The distinction in measures helps interpret the potential roles of different traveller groups or countries on importation risk. For example, model results suggest that essential travellers had a substantially higher PP than non-essential travellers during the study period. This difference can largely be attributed to pre-departure testing requirements for non-essential travellers as supported by results from the counterfactual analyses. However, despite higher PP in essential travellers than non-essential travellers, the overall number of imported cases from essential travellers was low because there were far fewer essential travellers. Another example from the country-level perspective has the opposite conclusion. Model output indicated that travellers from the USA contributed the highest number of imported cases because travel volumes from the USA were higher than any other country, despite the PP of travellers from the USA being lower compared to other countries (e.g. Mexico, Brazil). We found using both measures together is more revealing of importation risk than relying on one alone.

As in [ 41 ], which demonstrates the effectiveness of the pre-departure testing program, our model suggests that there would have been nearly twice as many importations estimated to occur in the absence of a pre-departure testing requirement (counterfactual scenario 2). It is important to note that model results are expected to be conservative in terms of the impact of pre-departure testing, given that the mean test sensitivity chosen in our model (i.e. 60%) fell on the lower range of plausible values. The temporal increase in the surplus cases that would have occurred had non-essential fully vaccinated travellers not undergone pre-departure testing (counterfactual scenario 1) can be attributed in part to a growing proportion of non-essential travellers becoming fully vaccinated through time. With vaccination, a larger number of travellers were exempt from the pre-departure testing requirement in counterfactual scenario 1, resulting in increased importations compared to the baseline scenario. The observed temporal increase in fully vaccinated travellers could be explained by the following factors: 1) increased second dose uptake within the Canadian population [ 42 ], 2) permitting fully vaccinated non-essential citizens and permanent residents of the US with a GoC approved vaccine to enter Canada for discretionary travel, with exceptions, effective August 9, 2021, and 3) extending factor #2 on September 7, 2021 to all other countries [ 8 , 14 ]. Consequently, toward the end of the study period, the difference in the impact of removing pre-departure testing in fully vaccinated non-essential travellers as opposed to all non-essential travellers was relatively small. While this analysis highlights the impact of the pre-departure testing program, it also demonstrates the versatility of the model in assessing and comparing the relative influence of different prevention strategies.

Although evaluating the impact of international COVID-19 importations on the local spread in Canada is beyond the scope of this paper, it has been explored previously in different contexts. Results from modelling studies suggest that case importation may have played an important role in local dynamics during the early phase of the COVID-19 pandemic and for emergent variants [ 19 , 20 , 43 ] or in countries with low prevalence and limited public health measures in place to restrict domestic spread [ 44 ]. However, international travel restrictions appear to be less effective once the disease is widespread and outbreaks are self-sustaining in the destination country [ 43 , 45 , 46 ]. In that specific context, imported cases would have a relatively small contribution to local transmission dynamics. As such, the impact of international travel restrictions relies on complex and dynamic factors, and requires evaluation and adaptation to the evolving local and global epidemiological situation, while also taking into account their economic and social costs. Previous work evaluating the potential impact of the border re-opening on disease spread within Canada [ 47 ] has been performed using an agent-based model [ 48 , 49 , 50 , 51 ]. However, further analyses would be needed to fully assess the impact of the pre-departure testing requirements on local transmission dynamics among the Canadian population.

Despite the strengths of our modelling approach there are important limitations to consider. First, for the study presented, we did not have access to border testing data for validating model results. Furthermore, as with any highly data driven model, error in input data will decrease accuracy of model output. For instance, the combination of multiple datasets to obtain air travel volume could have led to biased model inputs by traveller group. However, these data sources had the advantage of accounting for Notices to Airmen (NOTAMs) on flight suspensions from specific countries during the study period. Furthermore, the model relies on robust global surveillance data. Poor data quality and quantity can result in biased outcomes, especially in countries with limited testing capacities and unreliable reporting systems. A strength of the current model is the incorporation of a modified semi-Bayesian probabilistic bias approach, implemented to correct the number of reported cases by adjusting for under-ascertainment [ 27 ]. Although the country-specific case count estimates from this methodology align well with other published estimates (Fig. A1 in Additional file 1 ), a minimal amount of data is still required to produce reliable results.

Other limitations arise from the model assumptions. First, by assuming that there was complete protection against reinfection and no-waning in post-infection- and vaccine-induced immunity, model output could underestimate importation risk. Secondly, it was assumed that Canadian travellers only visit one country (the country of departure) and for a limited period prior to departure for Canada and that foreign travellers remain in their respective country of departure without travelling to other countries throughout the pandemic. We justify these assumptions because travel was greatly reduced during the pandemic [ 52 , 53 ]. Also, we erred on a simplified model structure in the absence of having complete data on travel history prior to departure for Canada. These assumptions likely reduced the accuracy in estimating travellers’ probabilities for vaccine- (for foreign essential travellers) and infection-acquired protection (for all travellers) and probabilities of exposure in the country of departure prior to travel. It is however difficult to know if the resulting error over- or underestimated importation risk. Finally, the model assumed that the traveller population was represented by the underlying country population in terms of the vaccination coverage (for essential travellers only), age demographics and socio-economic landscape, which could potentially lead to bias in terms of estimated exposure risk. For instance, travellers departing from countries with large wealth and income inequalities may have higher quality housing (i.e. less overcrowding) and better access to vaccination, and hence lower SARS-CoV-2 exposure compared to the general population from which model estimates for infection probabilities were calculated [ 54 ].

Our mathematical model provided a detailed COVID-19 importation risk profile for air travellers arriving at Canadian airports from international departures. Model outputs indicated travel groups and countries contributing high importation risk as measured by the number of imported cases and PP. Essential travellers were estimated to contribute fewer importations than non-essential travellers. Furthermore, model results suggest that pre-departure molecular testing in non-essential travellers likely led to lower numbers of imported cases and PP than when compared to counterfactual scenarios that were more lenient. The model we present here was applied to a Canadian COVID-19 context, including an assessment of pre-departure testing, but could be adapted to other similar infectious diseases and border measures, such as vaccination mandates on specific traveller groups and flight suspensions from high-risk countries. As the rate of emerging infectious diseases continues to increase with global environmental change [ 55 ], versatile tools such as this importation risk model can help support evidence-based border policy development.

Availability of data and materials

The data that support the findings of this study are available from CBSA, IATA, and GISAID but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of CBSA, IATA, and GISAID.

Abbreviations

Canada Border Services Agency

International Air Transport Authority

Government of Canada

Gross National Income

Our World in Data

Percent Positivity

Variants of concern

Variants of interest

Notice to Airmen

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Acknowledgements

We would like to thank Samir Mechai for his help in processing the weekly GISAID data on the COVID-19 variants, Dige Guan for providing aggregated data from ArriveCan and ContactTrace, David Champredon for support in the calculation of a mean test sensitivity estimate and Christopher Bell, Kerry Watkins, Rachel Rodin, Elizabeth Harris, Daniele Curtis, and Shirley Bryan for providing critical review and comments on the manuscript.

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Rachael M. Milwid and Vanessa Gabriele-Rivet contributed equally to this work and share first authorship.

Authors and Affiliations

Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, St-Hyacinthe, QC, Canada

Rachael M. Milwid, Vanessa Gabriele-Rivet, Nicholas H. Ogden, Patricia Turgeon & Erin E. Rees

Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Guelph, Guelph, ON, Canada

Aamir Fazil

Department of Pathology and Microbiology, Faculty of Veterinary Medicine, Université de Montréal, Saint-Hyacinthe, QC, Canada

Nicholas H. Ogden, Patricia Turgeon & Erin E. Rees

Physique Des Particules, Université de Montréal, Faculté Des Arts Et Des Sciences, Montréal, QC, Canada

David London

Emergency Management Branch, Global Public Health Intelligence Network Tiger Team, Public Health Agency of Canada, Ottawa, ON, Canada

Simon de Montigny

Epidemiology of Zoonoses and Public Health Research Unit, Faculté de médecine vétérinaire, Université de Montréal, Saint-Hyacinthe, QC, Canada

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ER, NO, VG-R, and RMM designed the study. ER, VG-R and RMM contributed to the model development and analysis. DL contributed to the equation formation and SDM provided support with interpretation of the results. VG-R, RMM and ER wrote the manuscript and ER, NO, VG-R, AF, PT, DL and SDM edited the final manuscript. VG-R and RMM contributed equally to this work and share first authorship. ER is the senior author.

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Correspondence to Vanessa Gabriele-Rivet .

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Milwid, R.M., Gabriele-Rivet, V., Ogden, N.H. et al. A methodology for estimating SARS-CoV-2 importation risk by air travel into Canada between July and November 2021. BMC Public Health 24 , 1088 (2024). https://doi.org/10.1186/s12889-024-18563-1

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