Welcome to Plugging the Gap (my email newsletter about Covid-19 and its economics). In case you don’t know me, I’m an economist and professor at the University of Toronto. I have written lots of books including, most recently, on Covid-19. You can follow me on twitter (@joshgans) or subscribe to this email newsletter here.
Today’s newsletter is about managing your contact budget. A contact budget is a term that I have seen thrown about for some months but it hasn’t really had a full treatment. Basically, a contact budget is an upper limit on the number of contacts you should have during a pandemic. It certainly is a term that is designed to draw an economist’s eye. But is there such a thing as a contact budget and, if so, what does it really look like?
If you don’t want to get Covid-19, you need to avoid contact with infectious people. That is easier said than done because you don’t know whether someone is infectious or not. Of course, if you really want to play it safe you can avoid contact with all people which will, by definition, also include infectious people. Somewhere in between contact with all people and avoiding contact with all people is a point where having some contacts makes sense. But what is that point?
A few months ago I imagined an app. The app would use Bluetooth on your phone to count other people you had contact with. They would all have the app. Then it would count and if you had too many contacts, it would tell you to budget. It sounds nice. But if you were developing that app what would you put in it as a contact limit? If I could put in the limit myself, what would it be?
In Toronto, where I live, there are currently about 1,500 confirmed people who have tested positive but not yet negative for the coronavirus. The flow is interesting. On any given day, we add 25-40 people to the infections pile. That’s not the GTA so it comes from a pool of about 3 million people. So on any given day, I may have a 0.0013% chance of contracting the coronavirus. On that score, it seems that trying to avoid people seems a bit much.
Of course, that is the number of infections coming from a population, most of whom are avoiding contacts. If I were to suddenly seek out people, I would be way above the average for the population and, moreover, because that is how things work, the people I might find for my contact spree would also be above average for the population. How much higher would my infection risk be? Possibly a lot higher but actually coming up with a calculation would seem to be challenging.
But to get a handle of that, suppose I wanted to get Covid-19 right now. Where, within a few hours travel, would I go? The news tells me that the closest big hotspot is Iowa which isn’t that far away. If I got there today, I would be mixing with a population where 1,000 in a million were getting infected each day. That gets me to a 0.1% infection chance each day. Is that worrisome? To find out, we have more work to do.
How about we come at this from another direction? What risk of becoming infected would cause me to want to avoid all contacts? Covid-19 seems like a crappy disease to get especially for someone like me who feels old every time I look at mortality statistics as a function of age. So let’s suppose that a one in a hundred chance of catching Covid-19 is enough for me.
But that 1% chance is not 1% each day but 1% over the next year or so. That is, if I want to live with a probability of greater the 99% that I will not have had Covid-19 over 365 days, if the daily probability of infection for me is p, I need the following to be true:
0.99 < (1 - p)^365 or p < 0.00275%
Well, that escalated quickly. It just over double the current Toronto rate and 36 times lower than the current Iowa rate. This tells me that I don’t want to be complacent about this.
How many contacts?
That probabilistic calculation gets us somewhere but what I really want to know in formulating my contact budget is how many people can I have contact with over what period?
Let’s start with where I am at the moment. I keep away from everyone pretty much except for my family. I won’t count them for the moment (and yes, I know that I am going to have to but let’s not let this away from us just yet). Over the course of a week, I have contact with 3-5 people from the person who cleans our house, the occasional electrician or whatnot, people walking dogs whom my dogs want to butt sniff, to neighbours and the cashier at the bakery. You might be wondering about grocery shopping but we have been pushed over to Instacart these days but that could easily add 20 people to the weekly mix. None of those are really close and rarely for any extended period of time.
But what if I wanted to do something like go to the movies? In that case, things get tricky. There may be 50 people in the movie theatre of unknown risk, another 20 theatre employees and another 5 people who might share an elevator with us. So there is 75 people right there from one 2 hour activity. If I wanted to go to a restaurant there would be more contacts too but not as much as that.
From this, we can see that it is these ‘events’ that really have the potential to expand the number of people you have contact with. It seems that those should be budgeted. But again, what is the rate? One of these every month, two weeks, or week? We need information there.
What about the family?
Now we come to the family. There is my spouse but she lives my hermit life but for a twice-weekly visit to the gym where she encounters 3 other people (it is small). She also goes to a book club once a month that adds another 5 people to the mix. Actually, that makes me start to wonder if she is trying to manage her contact with me!
Nonetheless, the real problem is the kids. One is off in another city so no problem there but another is doing college remotely from home and the other is doing high school. The remote college puts my son in the same category as my spouse in terms of contacts. The higher schooler will soon be another matter entirely.
She is going to go to school every other day. Usually, she would take public transport but we have decided to drive her instead to reduce exposure. Her school has 400 students, so she will be in a group of 200 but won’t have contact with all of them. With a bit of luck it will be down to 30. But that is 30 kids everyday and their own networks. This is clearly the point where the household contact budget is going to face some problems.
At this point, the idea of scientifically arriving at a total number of contacts for a household for, say, a two week period seems pretty futile. All we know is that we should be managing contacts but there is not enough information to give us a range we should keep to.
What’s an economist who wants to budget and trade-off options supposed to do? Aaron Carroll in the New York Times urges us to continue to try and trade-off things lest we fall into ‘all or nothing’ type behaviour. He writes:
Each decision we make to reduce risk helps. Each time we wear a mask, we’re throwing some safety on the pile. Each time we socialize outside instead of inside, we’re throwing some safety on the pile. Each time we stay six feet away instead of sitting closer together, we’re throwing some safety on the pile. Each time we wash our hands, eat apart and don’t spend time in large gatherings of people, we’re adding to the pile.
If the pile gets big enough, we as a society can keep this thing in check.
Carroll’s point was that we should be less frustrated at the few people not doing what they should and start appreciating what people are doing.
To keep the pile big enough, though, we need to be willing to trade some activities for others. If people want to play on a sports team, for instance, they should consider giving something up to do so. Increasing their risk by participating in a group activity should prompt them to reduce their risk the rest of the time. …
We could choose to engage in just some of those things. We could decide to get a massage or get our nails done or have a haircut — instead of demanding that all of these and more be available to us simultaneously.
This is good advice. It is a heuristic. It isn’t exact. But it is a way of managing contacts even if we don’t know how much we really have in our contact accounts.
That said, it is tricky. For instance, Carroll uses this logic to argue with his daughter about visits with friends:
My daughter argues that as long as she’s seeing all of her friends together in school, they should be able to gather together in their houses as well. Unfortunately, she has risk exactly backward. She’s not alone; lots of Americans do.
My kids, like most in Indiana, have been back at school since mid-August. Each time my 9th and 11th grader head off to high school, they spend more time among other human beings in a day than they had cumulatively all summer. Because of that, they along with many of their friends and those friends’ parents think that there’s less reason to be careful in other aspects of their lives.
But as we loosen restrictions in some areas, we should be increasing restrictions in others. If kids are going to take on more risk at school, they should find ways to be even safer outside of it. Large groupings at a friend’s house are not a good idea.
I am not sure she has it quite backwards. If you go to school with a friend, is it risky to see that same friend on the weekend or someone else? If your friend was infected on Wednesday, you have about as much chance of being infected on Saturday and you can’t get infected twice. But if some other person was infected on Wednesday and you see them on Saturday, your additional risk of becoming infected is surely higher.
What is true is that if you are seeing people at school you should see fewer other people at weekends. This is why going to school and then going to another weekend sports activity is likely worse than going to a school sports activity (without external teams).
In the end, the advice we have here is to be mindful. If someone in your household does attend a wedding, then perhaps everyone has to hold off on events for two weeks. If you want to go to the movies, go together and then hold off on other events for two weeks. And if someone is going to school, then you need to hunker down for the sake of everyone going to school.
That said, I still wouldn’t mind having that contact counting app. I’d love to at least obsess over the data.