One large gathering is riskier than 10 small ones: the math of COVID-19 spread

Many of us may have forgotten high school math, but understanding how relationships—linear, quadratic, and exponential—work can help us better assess risks in our daily lives. As the world gradually reopens, it’s crucial to think beyond basic assumptions and recognize that some activities carry far more danger than others, even if they seem similar at first glance.

It’s important to remember that even small actions can add up. Just because you’ve already taken a risk by going to the grocery store doesn’t mean you should stop taking precautions altogether. Most of us understand that risk exists on a spectrum. Even at a crowded event, wearing a mask and washing hands still makes a difference. And while dining out is generally safer than eating indoors in a packed restaurant, it’s still smarter to choose outdoor seating whenever possible.

But here’s the thing: even these risk levels can be confusing. It’s tempting to think, “Maybe going to two events is only twice as bad as one?” The truth is, the math behind how the virus spreads doesn’t work that way. Instead, it follows nonlinear patterns—meaning the risk increases faster than we might expect.

Quick note: The WHO has never said that asymptomatic people can’t spread the virus. That’s an important fact to keep in mind as we navigate public health guidelines.

Some Risks Grow Quadratically

Let’s take a look at how the number of people at an event affects the risk of transmission. Imagine three gatherings with 10, 50, and 100 people respectively. When people interact, each pair of individuals forms a "contact pair," which is a potential opportunity for the virus to spread.

The number of contact pairs grows in a quadratic way—roughly proportional to the square of the number of attendees. Here’s a breakdown:

This means that a gathering of 100 people poses significantly more risk than one with just 10. And this doesn’t even account for the possibility of a superspreader being present, which can make things spiral out of control very quickly.

So, it’s not just about how many people are there—it’s also about how those people interact and where they go next. That’s why smaller, more controlled gatherings are often safer than large, unstructured events.

Other Risks Grow Exponentially

Now let’s consider what happens if someone is contagious before showing symptoms. Suppose you get infected and spread the virus for a week without knowing it. During that time, you attend a few events with 10 people each. But here’s the catch: those 10 people might also go to other events, and so on.

The chain of exposure doesn’t grow linearly—it grows exponentially. If you and nine friends go to one dinner, you’re exposed to 9 people. But if everyone goes to two events, that number jumps to 100. And if each of those people then attends another two events, the total could reach 1,000 in no time.

This is why it’s so important to limit both the size of your social circles and how frequently you meet new people. Repeating interactions with the same group reduces the chance of spreading the virus widely.

The Bottom Line: Understand the Math, Make Smarter Choices

Reopening isn’t a binary choice. There are many ways to stay connected while keeping risks low. We don’t have a fixed limit on how much we can do, but we do have a responsibility to understand how different activities affect the spread of the virus.

Communities can reduce overall risk by promoting low-risk behaviors—like outdoor meetings, mask-wearing, and limited group sizes—rather than allowing even a small amount of high-risk activity. With a better grasp of how the virus spreads, we can open up safely and responsibly.

For more on how to assess and manage your own risk, check out these related stories:

• Doctors rank activities by COVID-19 risk
• State of the Pandemic, June 2020, Part I: What we know about SARS-CoV-2
• How to think about your risk factors for severe illness if you get COVID-19
• The CDC’s reopening plan was shelved, but we can still use it
• Fact-checking the CDC’s new guidance: you should still disinfect packages [Updated]

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