When you encounter groups of people in public, what’s the probability that at least one of those people has COVID-19? Last weekend I went shopping at Costco. It was packed. I’m guessing I personally encountered about 100 people. Later that evening I made a quick trip to Sprouts, a local supermarket where I encountered about 10 people. I wondered: what’s the likelihood that I encountered someone who was COVID-positive? And how did the risks of those two experiences compare?
Let’s look at the data. The first thing we need to determine is the prevalence of COVID-19 in our area of interest. Or more concretely, what is the probability that any randomly selected person in the area will be COVID-19 positive?
The stores I visited were in the 92128 zip code. The County of San Diego publishes zip code level data on case rates. In the 92128 zip code, the case count on July 22nd is 317 cases per 100,000 residents.[1] That’s about 1 in 315 people.
It is widely recognized that many cases are going undetected. According to the CDC, actual cases counts are 6 to 24 times higher than the official positive cases. In a survey of multiple cities, the most common multiple was actual case counts 10 times higher than the official counts. I will use the 10X assumption.[2]
These numbers represent the total number of positive cases. However, many of those cases have been resolved, either because the patient recovered or died. I could not find zip code level data for recoveries, so instead I used the overall San Diego numbers to estimate active cases. 29% of all cases in San Diego are currently active. Hence, I assume that 29% of the 92128 cases are active.[3]
I recognize that these are estimates. However, that is more than satisfactory for my purposes. We are much more interested in rough accuracy than high precision.
With these assumptions, we find that approximately 1 in 109 people are currently infected with COVID-19 in the 92128 zip code. Does that seem pretty low? What does that actually mean in terms of the risk of encountering a COVID-positive person?
During the Costco and Sprout visits, I estimate that I encountered roughly 100 people and 10 people, respectively. How does this translate to risk? I will explain the methodology behind the calculations below (for those interested). The bottom line is, under these assumptions for the 92128 zip code on July 22nd:
The probability of encountering someone COVID-19 positive in a group of 100 people is about 60%. In a group of 10 people, the probability is almost 10%.
You might be interested in estimating the risk for a broader range of activities and numbers of people encountered. The figure below displays the probability as a function of the number of people encountered from 0 to 500 people.
We can do the same analysis for San Diego County overall, as well as Los Angeles County and the state of California overall. I note that Los Angeles has been hit particularly hard.
We use the following assumptions and data sources, as of July 22nd 2020:
For San Diego County:
For Los Angeles County:
For California overall:
With these assumptions, we find that approximately 1 in 46 people in San Diego County are currently infected with COVID-19. In Los Angeles County, it’s 1 in 9 people. For California overall, it’s 1 in 14 people. Clearly, Los Angeles has been hit much harder than San Diego, and even within San Diego, the prevalence of COVID infections varies significantly.
How does that translate to risk as we increase the number of people encountered? The table below summarizes the results. Note that in San Diego County overall, encountering only 10 people results in a 20% probability of encountering someone COVID-positive, about 2X the rate in the 92128 zip code. If we encounter 100 people, the probability increases to almost 90%. In Los Angeles, encountering only 10 people results in almost a 70% probability of encountering someone COVID-positive!
The figure below displays the probabilities for San Diego County, Los Angeles County, and California overall as a function of the number of people encountered.
Here I provide a brief summary of the methodology underlying these calculations. The active case rate per capita (let’s call that R) tells us the probability that any one randomly selected individual in a region is COVID-positive. If we encounter N people, it is possible that anywhere from 0 to N of these people are COVID-positive. We need to know the probability that we will encounter anywhere from 1 to N people who are COVID-positive.
To simplify the calculation, we can first calculate the probability that we encounter 0 people who are COVID-positive. The sum of all possibilities (the probability of 0 positives, 1 positive, 2 positives, all the way through N positives) must equal 1. Hence, the probability that we encounter at least 1 person who is COVID positive (probability of 1 to N positives) will be 1 minus the probability that we encounter exactly 0 people who are COVID-positive.
The probability that we encounter exactly 0 people who are COVID-positive is the probability that each individual is NOT positive (1 – R) raised to the power of the number of people encountered, N.
Hence, the probability that we encounter at least one person who is COVID-positive is:
The probability of encountering someone in public who is COVID-19 positive depends on the number of actual active cases per capita in the region and the number of people encountered. The active cases per capita varies significantly across different regions. In addition, the case rate is dynamic and changes within each region over time. The key takeaways are:
(1) Especially in areas with active outbreaks, the likelihood of encountering someone COVID-19 positive is quite high, and
(2) This highlights the importance of social distancing and widespread mask-wearing to reduce viral exposure and the chances of becoming infected.
Stay safe!
When you encounter groups of people in public, what’s the probability that at least one of those people has COVID-19? Last weekend I went shopping at Costco. It was packed. I’m guessing I personally encountered about 100 people. Later that evening I made a quick trip to Sprouts, a local supermarket where I encountered about 10 people. I wondered: what’s the likelihood that I encountered someone who was COVID-positive? And how did the risks of those two experiences compare?
Let’s look at the data. The first thing we need to determine is the prevalence of COVID-19 in our area of interest. Or more concretely, what is the probability that any randomly selected person in the area will be COVID-19 positive?
The stores I visited were in the 92128 zip code. The County of San Diego publishes zip code level data on case rates. In the 92128 zip code, the case count on July 22nd is 317 cases per 100,000 residents.[1] That’s about 1 in 315 people.
It is widely recognized that many cases are going undetected. According to the CDC, actual cases counts are 6 to 24 times higher than the official positive cases. In a survey of multiple cities, the most common multiple was actual case counts 10 times higher than the official counts. I will use the 10X assumption.[2]
These numbers represent the total number of positive cases. However, many of those cases have been resolved, either because the patient recovered or died. I could not find zip code level data for recoveries, so instead I used the overall San Diego numbers to estimate active cases. 29% of all cases in San Diego are currently active. Hence, I assume that 29% of the 92128 cases are active.[3]
I recognize that these are estimates. However, that is more than satisfactory for my purposes. We are much more interested in rough accuracy than high precision.
With these assumptions, we find that approximately 1 in 109 people are currently infected with COVID-19 in the 92128 zip code. Does that seem pretty low? What does that actually mean in terms of the risk of encountering a COVID-positive person?
During the Costco and Sprout visits, I estimate that I encountered roughly 100 people and 10 people, respectively. How does this translate to risk? I will explain the methodology behind the calculations below (for those interested). The bottom line is, under these assumptions for the 92128 zip code on July 22nd:
The probability of encountering someone COVID-19 positive in a group of 100 people is about 60%. In a group of 10 people, the probability is almost 10%.
You might be interested in estimating the risk for a broader range of activities and numbers of people encountered. The figure below displays the probability as a function of the number of people encountered from 0 to 500 people.
We can do the same analysis for San Diego County overall, as well as Los Angeles County and the state of California overall. I note that Los Angeles has been hit particularly hard.
We use the following assumptions and data sources, as of July 22nd 2020:
For San Diego County:
For Los Angeles County:
For California overall:
With these assumptions, we find that approximately 1 in 46 people in San Diego County are currently infected with COVID-19. In Los Angeles County, it’s 1 in 9 people. For California overall, it’s 1 in 14 people. Clearly, Los Angeles has been hit much harder than San Diego, and even within San Diego, the prevalence of COVID infections varies significantly.
How does that translate to risk as we increase the number of people encountered? The table below summarizes the results. Note that in San Diego County overall, encountering only 10 people results in a 20% probability of encountering someone COVID-positive, about 2X the rate in the 92128 zip code. If we encounter 100 people, the probability increases to almost 90%. In Los Angeles, encountering only 10 people results in almost a 70% probability of encountering someone COVID-positive!
The figure below displays the probabilities for San Diego County, Los Angeles County, and California overall as a function of the number of people encountered.
Here I provide a brief summary of the methodology underlying these calculations. The active case rate per capita (let’s call that R) tells us the probability that any one randomly selected individual in a region is COVID-positive. If we encounter N people, it is possible that anywhere from 0 to N of these people are COVID-positive. We need to know the probability that we will encounter anywhere from 1 to N people who are COVID-positive.
To simplify the calculation, we can first calculate the probability that we encounter 0 people who are COVID-positive. The sum of all possibilities (the probability of 0 positives, 1 positive, 2 positives, all the way through N positives) must equal 1. Hence, the probability that we encounter at least 1 person who is COVID positive (probability of 1 to N positives) will be 1 minus the probability that we encounter exactly 0 people who are COVID-positive.
The probability that we encounter exactly 0 people who are COVID-positive is the probability that each individual is NOT positive (1 – R) raised to the power of the number of people encountered, N.
Hence, the probability that we encounter at least one person who is COVID-positive is:
The probability of encountering someone in public who is COVID-19 positive depends on the number of actual active cases per capita in the region and the number of people encountered. The active cases per capita varies significantly across different regions. In addition, the case rate is dynamic and changes within each region over time. The key takeaways are:
(1) Especially in areas with active outbreaks, the likelihood of encountering someone COVID-19 positive is quite high, and
(2) This highlights the importance of social distancing and widespread mask-wearing to reduce viral exposure and the chances of becoming infected.
Stay safe!
