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Let’s say you wanted to figure out to what extent the recent social justice protests contributed to the spread of the coronavirus in Utah. How would you do it?

It’s a complicated question, because there are significant reasons you might expect infections to spread like wildfire in protests:

1. Huge crowds of people not socially distanced. As we know, that’s a major ingredient of a superspreading event.

2. These protests often lasted for hours, enough time to spread the virus in previous superspreading events.

3. Lots of chanting and shouting — an action that has proved to spread the coronavirus. Just one minute of loud speech can emit 1,000 coronavirus-laden droplets, which then can linger in the air for up to eight minutes, according to a U.S. study released in May.

But there are also several mitigating factors:

1. The protests took place outdoors, allowing the droplets containing the virus to disperse or evaporate. Even opening a window is a key step in keeping viral droplets from lingering. One early study of 1,245 coronavirus cases in China found that only one instance of transmission occurred outdoors: a close conversation where two men also shook hands.

2. The majority of protests also occurred during the day in June, which means sunlight was at play. When exposed to simulated sunlight in a lab, 90% of the virus was inactivated every 6.8 minutes.

3. Mask usage was relatively common in the protests. While there isn’t really data on how widespread usage was, protest organizers made great efforts to distribute masks in Utah. The political party that wears masks more frequently was also more likely to participate in the protests.

4. Some people likely decided to stay home due to the protests rather than go out. People certainly stayed home as a result of the curfew set in Salt Lake City.

So which set of factors won out?

Probably the crudest possible way to find out is to look at the graph of coronavirus cases since May 29, the day of the first protest. And, yes, cases have gone up significantly since that date.

But, of course, there are other reasonable explanations for the June jump. More businesses opened, including some high-risk ones like bars and movie theaters. People took fewer precautions, spending more money in restaurants, for example. More Utahns went back to work. Some areas of the state went to green in the month, though those were rural counties far away from urban Salt Lake City.

Another way to investigate the question is to compare the size of the protests in each city, and see if it correlates with coronavirus spread in those areas. That’s what a paper released this week by the National Bureau of Economic Research did: It took the 315 largest U.S cities, and compared the state of the coronavirus in the 10 days before George Floyd was killed and then the 25 days after. Do places like Minneapolis see big case growth?

Typically, 25 days has been enough to detect past differences in case growth. Social distancing measures were shown to make a difference in cases just five to 10 days after being enacted, while another paper showed growth in cases two weeks after local universities took spring breaks. If a difference in growth was detectable, 25 days is enough to detect it.

Instead, the researchers found zero difference in case growth in cities with big protests compared to cities with small or no protests. In particular, their confidence intervals meant they were at least 95% confident that any difference was less than 0.5 percentage point — not only did they find zero difference, they were quite sure of it.

They then looked to see if there was any difference in the coronavirus between cities in which protests were persistent over many days and where they were not. No difference. They looked to see if there was a difference where protests were violent. Still, no difference. Finally, they looked to see if there was a difference in cities where curfews were ordered. No difference.

Interestingly, the researchers also found that there was an increase in social distancing as a result in the protests — not by much, but by about 2%. People stayed at home more than they did in the week or two leading up to the protests. This might have been enough to mitigate whatever additional cases big protests would have added.

Of course, just because something is true over the aggregate nationally doesn’t make it so locally. The biggest protests were in Salt Lake City proper, rather than the surrounding areas. If protests caused coronavirus growth, we would probably expect to see greater proportional growth in Salt Lake City than the rest of the county. Thanks to Salt Lake County’s city-by-city coronavirus data, we can do that comparison.

I don’t see any bigger growth in Salt Lake City than the rest of Salt Lake County, proportionally. Over the aggregate, growth looks pretty equal, if anything, it might be a tad greater in the non-SLC parts of the county.

If you’re a journalist, there is an even more direct approach you can take to find out if the coronavirus spread significantly due to the protests in Salt Lake County: You can just email the health department and ask.

After all, the health department does extensive contact tracing for every coronavirus case, calling and asking each a series of questions to try to figure out where each case was infected. We’re really quite good at contact tracing in Utah: We’ve been able to find a specific source for over 70% of cases week after week.

Nicholas Rupp, communications manager at the Salt Lake County Health Department, told me that the department had found just five cases that “may be tied to attending a large community gathering like a protest.”

“These people became ill after attending such an event,” Rupp said, “and our epidemiologists have not identified any other likely source of infection.”

Given that there have been 4,613 positive cases in Salt Lake County in June, according to the health department, and thousands of people who attended protests over the course of multiple weeks, only five cases tied to the protests is an exceptionally low number. To echo the authors of the National Bureau of Economic Research paper, I would bet that those five cases were made up for by the slight increase of people staying at home due to Salt Lake City curfews in the days after the biggest protests.

We can take some lessons for other activities here as well. During the summer months, doing things outside with a mask on is low risk — the virus disperses and dies so quickly under those conditions. It’s even enough to significantly mitigate high-risk activities like crowding and shouting. Of course, I recommend maintaining physical distance when possible as well.

On the other hand, it shows how dangerous other forms of carelessness can be: If our increase in cases isn’t due to the protests, it’s due to other factors. That means indoor transmission is the culprit — at bars and restaurants, all types of workplaces, and in our homes. We need to be vigilant in those places: Closed spaces with poor ventilation are especially dangerous.

Outdoor protests, though? I think we can safely conclude: They weren’t the source of our worrying coronavirus growth.