Calculating the probability of getting COVID
July 14, 2020 6:08 PM Subscribe
So I was trying to guesstimate as a thought experiment the odds of catching COVID in a grocery store here in Ottawa. I got to a certain spot but then I got stuck. What's the best way forward? Here's what I have so far....
Assume 10,000 infected, mobile citizens in all of Ottawa.
My Independent grocery store allows 100 people inside at any one time.
The grocery store serves a population of 20,000 people out of the 900,000 people in Ottawa. Number of infected people in the grocery store's customer base = (20K/900K) * 10,000 infected = 220 infected. Odds of at least one infected in the store = 1 - (19,780/20000)**100 = 66 percent.
Here's the difficulty - what's my probability of catching COVID from the infected ones in the store? All I have at this point is that the number of infected inside is > 1 and <=100. What would be a good way to simplify the question to get to a probability estimate?
Assume 10,000 infected, mobile citizens in all of Ottawa.
My Independent grocery store allows 100 people inside at any one time.
The grocery store serves a population of 20,000 people out of the 900,000 people in Ottawa. Number of infected people in the grocery store's customer base = (20K/900K) * 10,000 infected = 220 infected. Odds of at least one infected in the store = 1 - (19,780/20000)**100 = 66 percent.
Here's the difficulty - what's my probability of catching COVID from the infected ones in the store? All I have at this point is that the number of infected inside is > 1 and <=100. What would be a good way to simplify the question to get to a probability estimate?
Is everyone wearing a mask? How is the store ventilated?
posted by pinochiette at 6:14 PM on July 14, 2020 [1 favorite]
posted by pinochiette at 6:14 PM on July 14, 2020 [1 favorite]
Response by poster: Everyone is masked. Store is big and ventilated. Number of people that might pass within 6 ft would be 3-5 for a duration of 5 sec each.
posted by storybored at 6:20 PM on July 14, 2020
posted by storybored at 6:20 PM on July 14, 2020
You're assuming the 10k infected people are evenly distributed across the population of Ottawa. We know from transmission dynamics over the last six months that this is not true.
I don't know enough about income inequity in Ottawa, but this overview from NPR uses Texas census tracts, and this article from Politico looks at NYC zip codes -- both demonstrate a pretty stark differential depending on where you live.
posted by basalganglia at 6:27 PM on July 14, 2020 [3 favorites]
I don't know enough about income inequity in Ottawa, but this overview from NPR uses Texas census tracts, and this article from Politico looks at NYC zip codes -- both demonstrate a pretty stark differential depending on where you live.
posted by basalganglia at 6:27 PM on July 14, 2020 [3 favorites]
You have to factor in that some number of infected people will not be grocery shopping. I think the guidance in Ontario is that if you have any of a huge list of symptoms you must stay in for 14 days or get a test. Plus some people will just be too sick to go to the store. So you only need to consider asymptomatic and pre-symptomatic individuals, which means the odds of an infected person in the store need to be lower.
In terms of getting a probability estimate, you might consider what's the chance you're close enough to the person in the store to be infected. So what's the chance that you're within 2 meters of the person.
I think that Toronto public health classifies contacts into low, med and high risk (see this guidance document. I think being 2m for a duration of 5 seconds while masked would fall into the "only transient interactions" and thus the "low risk" category, and you would just need to self monitor for symptoms. So the Ontario Public Health thinks the chance of catching it is pretty low.
posted by ice-cream forever at 6:36 PM on July 14, 2020 [2 favorites]
In terms of getting a probability estimate, you might consider what's the chance you're close enough to the person in the store to be infected. So what's the chance that you're within 2 meters of the person.
I think that Toronto public health classifies contacts into low, med and high risk (see this guidance document. I think being 2m for a duration of 5 seconds while masked would fall into the "only transient interactions" and thus the "low risk" category, and you would just need to self monitor for symptoms. So the Ontario Public Health thinks the chance of catching it is pretty low.
posted by ice-cream forever at 6:36 PM on July 14, 2020 [2 favorites]
At the end of your calculation, you're going to wind up with some odds of interacting with some number of people with covid.
Imagine you are going to interact with one person and there's an x% chance they have covid, what are the odds that you will get it? If the interaction is "spend 48 hours making out together in a portapotty", the answer is very close to x%. If the interaction is "watch their YouTube video", the answer is very close to 0%.
There have been plenty of reports of outbreaks at grocery stores - amongst employees, who spend 8+ hours together, day after day, who talk to each other, share break rooms and bathrooms and so on. A lot of these outbreaks are on the order of 3 people, out of dozens working there. There have been very few (I've never seen any) reports of outbreaks amongst shoppers.
If you shop during relatively quiet times, ie when you can keep your distance from other shoppers and particularly when you don't have to wait in line spending several minutes near one or two people, and if most people (especially the cashier, the one person you do spend time near) wear masks, your odds of getting infected are very close to 0.
And if the final step in the calculation is multiply by zero, it doesn't matter how complex the calculation is before.
posted by Homeboy Trouble at 7:19 PM on July 14, 2020 [7 favorites]
Imagine you are going to interact with one person and there's an x% chance they have covid, what are the odds that you will get it? If the interaction is "spend 48 hours making out together in a portapotty", the answer is very close to x%. If the interaction is "watch their YouTube video", the answer is very close to 0%.
There have been plenty of reports of outbreaks at grocery stores - amongst employees, who spend 8+ hours together, day after day, who talk to each other, share break rooms and bathrooms and so on. A lot of these outbreaks are on the order of 3 people, out of dozens working there. There have been very few (I've never seen any) reports of outbreaks amongst shoppers.
If you shop during relatively quiet times, ie when you can keep your distance from other shoppers and particularly when you don't have to wait in line spending several minutes near one or two people, and if most people (especially the cashier, the one person you do spend time near) wear masks, your odds of getting infected are very close to 0.
And if the final step in the calculation is multiply by zero, it doesn't matter how complex the calculation is before.
posted by Homeboy Trouble at 7:19 PM on July 14, 2020 [7 favorites]
Also: Where are you getting "10,000 infected, mobile citizens in all of Ottawa?"
If you check out this page from Ottawa Public health, there have been 2166 cases in total ever in Ottawa. Active cases is currently 62.
posted by ManInSuit at 7:20 PM on July 14, 2020 [2 favorites]
If you check out this page from Ottawa Public health, there have been 2166 cases in total ever in Ottawa. Active cases is currently 62.
posted by ManInSuit at 7:20 PM on July 14, 2020 [2 favorites]
The COVID-19 Event Risk Assessment Planning Tool from GA Tech gives the estimated chance that at least 1 COVID-19 positive individual will be present at an event, given the size of the event (in your case, 100 customers plus some estimate of the staff present in the store). It's US-only but perhaps you can find a county with similar population and infection rate to compare. You'd still need some further calculation to get the probability of catching COVID-19 from that individual, which would depend on a lot of factors (mask compliance, social distancing, etc.) but it's a start.
posted by bunnysquirrel at 7:22 PM on July 14, 2020 [3 favorites]
posted by bunnysquirrel at 7:22 PM on July 14, 2020 [3 favorites]
Everyone is masked. Store is big and ventilated. Number of people that might pass within 6 ft would be 3-5 for a duration of 5 sec each.
If this is the case - I think the total number of people in the store is irrelevant to your calculation. Your math problem is "What are the odds of getting Covid from a 5-second interaction with 3 to 5 random residents of Ottawa".
(I am with Homeboy Trouble: You are multiplying two numbers which are both very, very close to zero.... No one knows what the odds are of getting Covid from a 5-second interaction with a masked stranger because, I think, no one knows of a single instance of that having ever happened....)
posted by ManInSuit at 7:31 PM on July 14, 2020 [8 favorites]
If this is the case - I think the total number of people in the store is irrelevant to your calculation. Your math problem is "What are the odds of getting Covid from a 5-second interaction with 3 to 5 random residents of Ottawa".
(I am with Homeboy Trouble: You are multiplying two numbers which are both very, very close to zero.... No one knows what the odds are of getting Covid from a 5-second interaction with a masked stranger because, I think, no one knows of a single instance of that having ever happened....)
posted by ManInSuit at 7:31 PM on July 14, 2020 [8 favorites]
I'd do the calculation in the other direction. There are about 1M people in Ottawa. Eyeballing the chart from Ottawa Public Health, it looks like about 100 new confirmed cases a month. Say that there are 500 total cases a month, because some of them may go undetected. So, in an average month, an average person has a 1 in 2000 chance of becoming infected.
The main unknown is how much one trip to the grocery store compares to the average amount of monthly interaction. Just as a guess, say it's 1%, or a third of the average daily interaction -- then the chance is roughly 1 in 200,000.
posted by ectabo at 7:50 PM on July 14, 2020 [2 favorites]
The main unknown is how much one trip to the grocery store compares to the average amount of monthly interaction. Just as a guess, say it's 1%, or a third of the average daily interaction -- then the chance is roughly 1 in 200,000.
posted by ectabo at 7:50 PM on July 14, 2020 [2 favorites]
I think you're counting the wrong population. I would hazard to guess that the most likely people in a grocery store to be infected are the people who work there, not the customers, because they're the ones who spend all day in the store, getting exposed to every customer who comes in. Your chance encounters probably don't result in an infection even if one of the people you pass by happens to be infected. The line-ups outside prevent line-ups at the cash register, which is probably the only place in the store where two customers would otherwise spend enough time in close proximity to infect each other.
posted by jacquilynne at 8:08 PM on July 14, 2020 [2 favorites]
posted by jacquilynne at 8:08 PM on July 14, 2020 [2 favorites]
Trevor Bedford (of the Seattle Flu Project and Fred Hutchinson Cancer Research Center) did a similar calculation to try to estimate the impact of protests on SARS-CoV-2 transmission. While nobody can say for certain, his admittedly very rough guess was that, on average, one infected person at a protest would transmit to one other individual per day. (This guess may have been an overestimate, as various evidence since then shows that protests had little or no impact on COVID-19 outbreaks.)
How does this compare to a grocery store? The average customer probably spends much less time at the grocery store than a protestor spends per day at a protest; maybe 1/4 as much. There are probably a lot fewer people packed into a given number of square meters; maybe 1/10 as many. Grocery store customers are much less likely to be shouting, signing, or breathing heavily from exercise, which are all known risk factors transmission. The indoor environment might lead to a greater buildup of droplets or aerosols, but on the other hand, grocery stores often have very large volume and good ventilation. Taking Bedford's guess as a starting point, and adjusting for the reduction in time spent in close contact with other people, one might take a wild guess that a grocery store would see one instance of transmission for every twenty or fifty infected customers.
This seems to line up with evidence from contact tracing showing that infection rarely occurs during shopping. (But as noted above, the risk is probably higher for the people work in the store.)
posted by mbrubeck at 8:29 PM on July 14, 2020
How does this compare to a grocery store? The average customer probably spends much less time at the grocery store than a protestor spends per day at a protest; maybe 1/4 as much. There are probably a lot fewer people packed into a given number of square meters; maybe 1/10 as many. Grocery store customers are much less likely to be shouting, signing, or breathing heavily from exercise, which are all known risk factors transmission. The indoor environment might lead to a greater buildup of droplets or aerosols, but on the other hand, grocery stores often have very large volume and good ventilation. Taking Bedford's guess as a starting point, and adjusting for the reduction in time spent in close contact with other people, one might take a wild guess that a grocery store would see one instance of transmission for every twenty or fifty infected customers.
This seems to line up with evidence from contact tracing showing that infection rarely occurs during shopping. (But as noted above, the risk is probably higher for the people work in the store.)
posted by mbrubeck at 8:29 PM on July 14, 2020
For estimating the number of currently-infected people, Youyang Gu’s model starts with the number of known deaths over time, uses some assumptions about the infection fatality rate (and duration of infection) to estimate backward to the number of infections in the past, and then uses an open-source SEIR model to estimate forward to the number of infections in the present and future.
For the entire province of Ontario, the model estimates about 12,000 currently infected people (0.1% of the population), and about 800 new infections per day. (This is about six times higher than the number of known cases. This result is in the same ballpark as various other methods of estimating the ratio of total infections to known cases.)
If this is accurate, and if the infection rate in Ottawa is similar to the province as a whole, then there would be about 1000 people currently infected in Ottawa.
posted by mbrubeck at 10:39 PM on July 14, 2020 [1 favorite]
For the entire province of Ontario, the model estimates about 12,000 currently infected people (0.1% of the population), and about 800 new infections per day. (This is about six times higher than the number of known cases. This result is in the same ballpark as various other methods of estimating the ratio of total infections to known cases.)
If this is accurate, and if the infection rate in Ottawa is similar to the province as a whole, then there would be about 1000 people currently infected in Ottawa.
posted by mbrubeck at 10:39 PM on July 14, 2020 [1 favorite]
I disagree with the SEIR model (which, as noted, is optimized for the US). Ontario has been testing around 25,000 people a day for a while, and our high death rate was due to the LTC outbreaks. I believe is is around 88% of people have been contacted by Public Health within a day of a postive test for contact tracing. Of the over 3 million people tested the test rate has been 3%, indicating there are few undetected cases in the community. I don’t think the number of undetected covid+ people is as high as that model predicts. It would be more accurate to look at the number of people hospitalized (currently 3) and extrapolate true infection numbers from that - which is pretty close to about 60ish people infected in the past two weeks. Also, compare where the transmission is occurring - the numbers are clear that in Ottawa it is institutional residents first, and secondly, health care workers are the unfortunate major victims. The exposure history is known in 98.5% of cases, so we have a really good handle on where the transmission is occuring, and the 10 cases a day is slightly higher than it has been.
In Ottawa, community transmission has been minuscule, so of the 10 daily cases yesterday, maybe 3-4 were from the community (which includes workplaces) and has been at that 3-4 cases a day for a couple of months. So, instead of assuming 10,000 infected, assume around 70 at the high end, the majority of whom know they are infected and self-isolating - so currently less than ten people in all of Ottawa who are possibly carriers and still walking around. Basically, your chance of being in the same shop at the same time is almost nil, and the chance of being near one of those ten people long enough to catch covid, especially if you are both wearing masks, is almost nil. Should you relax completely? No, but it is reasonable to accept there is a very small risk and not stress yourself by catastrophizing.
posted by saucysault at 12:58 AM on July 15, 2020 [4 favorites]
In Ottawa, community transmission has been minuscule, so of the 10 daily cases yesterday, maybe 3-4 were from the community (which includes workplaces) and has been at that 3-4 cases a day for a couple of months. So, instead of assuming 10,000 infected, assume around 70 at the high end, the majority of whom know they are infected and self-isolating - so currently less than ten people in all of Ottawa who are possibly carriers and still walking around. Basically, your chance of being in the same shop at the same time is almost nil, and the chance of being near one of those ten people long enough to catch covid, especially if you are both wearing masks, is almost nil. Should you relax completely? No, but it is reasonable to accept there is a very small risk and not stress yourself by catastrophizing.
posted by saucysault at 12:58 AM on July 15, 2020 [4 favorites]
ectabo's 1 in 200,000 figure seems like a sane best guess: it would mean that your own chance of catching the virus during an individual shopping trip would be very small - but that multiplied to a city wide level it might be sufficient for a small number of Ottawa's 100 cases per month to have originated that way. All the anti-infection measures which might be taken by you, other shoppers, staff or store owners - should mean the odds of any particular event causing you to be infected are all heavily suppressed from whatever value they would be without them. But those odds will not be zero.
posted by rongorongo at 5:04 AM on July 15, 2020
posted by rongorongo at 5:04 AM on July 15, 2020
If anything, I think 1 in 200,000 is probably too high. If most of the cases in Ottawa are detected in tests, then there may only be 100-200 new infections a month, and I think saucysault is right to focus on community transmission, which may be a fraction of that. The number of new cases per month acquired by supermarket customers might be only 0-5 or so, which would make the risk of a single supermarket trip under 1 in a million. And that risk can be reduced by taking personal precautions.
posted by ectabo at 6:14 AM on July 15, 2020
posted by ectabo at 6:14 AM on July 15, 2020
Nobody knows, because we don't know the last number you need: what's the rate of infection transmission for a single brief interaction where both parties are masked? The best evidence for that number being very, very low comes from looking at exposures in a different context: hospital settings where patients are tested when they come in and treated as if they are infected until the results come back in a few hours. In that setting, I found it very useful and reassuring to hear that in mid-April, at a point where UCHealth here in Denver had dealt with several dozen COVID patients (of the hundreds hospitalized across the state) and most staff were only wearing surgical masks, there were zero reported cases of patient to staff transmission. I've been intermittently looking for an update on that statistic (or a similar one from a different setting) now that more time has passed, because I think it's a very useful one for thinking about best case mask compliance risk assessment.
posted by deludingmyself at 9:00 AM on July 15, 2020
posted by deludingmyself at 9:00 AM on July 15, 2020
Nobody knows, because we don't know the last number you need: what's the rate of infection transmission for a single brief interaction where both parties are masked?
We may not know that number, but we know it's insanely low, because grocery stores and plenty of others have never closed in the US, and counts of cases do not at all correlate with people doing basic shopping. We know asymptomatic carriers exist; so we know that people with covid-19 have gone shopping.
They correlate well with continuous close contact, indoors or outdoors. They don't correlate with A/C either. In the US, they do correlate strongly with social-economic status, so the location of your grocery store matters. Not sure if that correlation in Ottawa is as strong.
posted by The_Vegetables at 1:56 PM on July 15, 2020 [3 favorites]
We may not know that number, but we know it's insanely low, because grocery stores and plenty of others have never closed in the US, and counts of cases do not at all correlate with people doing basic shopping. We know asymptomatic carriers exist; so we know that people with covid-19 have gone shopping.
They correlate well with continuous close contact, indoors or outdoors. They don't correlate with A/C either. In the US, they do correlate strongly with social-economic status, so the location of your grocery store matters. Not sure if that correlation in Ottawa is as strong.
posted by The_Vegetables at 1:56 PM on July 15, 2020 [3 favorites]
This thread is closed to new comments.
posted by storybored at 6:14 PM on July 14, 2020