As lockdown restrictions are relaxed and people go out more, what is the probability of actually encountering someone who has Covid-19 and is contagious?
Someone who has Covid-19 is infectious for 14 days but may not show symptoms for first 5 days (the mean). Once they have symptoms they will be either in quarantine or in the hospital. So your risk of encountering someone who is contagious is during the 5 days before they had symptoms. But there is no way of knowing how many such people there are, it may take up to 5 days before they have symptoms and can be counted. As a good approximation you can use the total number of new cases in the last 5 days.
In addition, many cases are unreported because people do not have any symptoms (asymptomatic) or their symptoms are so mild that they don’t realize they are sick. So add 10 times the total 5 day case count to include the unreported cases, based on this CDC analysis.
https://www.nytimes.com/2020/06/27/health/coronavirus-antibodies-asymptomatic.html?referringSource=articleShare
Then divide by the population of your location to get the probability that any random person is infected.
For Toronto this probability is .07% about 7 out of 10,000.
Rather than meeting a single person, what about meeting another couple at a restaurant where there are two more couples at adjoining tables and one server?
Using high school math you can calculate the probability that one or more of these 7 people are contagious.
This probability is .5% about 1 out of 200.
This is a fairly low risk of encountering someone who could infect you. There is additional risk of airborne infection but not enough is known to estimate its probability (see previous blog).
But the more people in a group, the higher the probability. If you go to a house party where there are 25 other people, the probability that at least one person is contagious is 1.7%
Low probabilities do not mean that you can skip the social distancing rules. If everyone does that it will increase the spread of the virus, slowly at first since it is low probability but more rapidly as cases increase and the probabilities increase.
