COVID-19 risks aren't straightforward—they don't simply double when the number of people doubles. For instance, four people gathered for dinner aren’t just twice as risky as two; they’re actually three times riskier. Many of us tend to avoid math like the plague (pun intended), but grasping concepts such as network effects and how linear, quadratic, and exponential relationships function can help us make smarter choices about risks as life starts to return to normal. After all, it's not like you've already been exposed by stepping out to buy groceries, so why not go ahead and start hugging street lamps? Most of us recognize that our COVID-19 risks exist on a spectrum. Even at crowded gatherings, wearing a mask and washing your hands remains crucial. Dining outdoors is far safer than sitting in a dim, cramped restaurant. However, there hasn't been enough discussion about how even these risk spectrums can be tricky to navigate. It’s tempting to think, “Well, maybe attending two events isn’t that much worse than one?†But unfortunately, the math doesn’t work that way due to the nonlinear nature of COVID-19 transmission.
More: The WHO never said asymptomatic individuals couldn’t spread the virus.
Some Risks Are Quadratic…
Let’s compare three events, all identical except for the number of attendees: 10, 50, and 100 people. When two people interact—whether talking or just passing by—it’s considered a "contact pair," an opportunity for the virus to spread. The number of contact pairs grows roughly quadratically with the number of people present. Here's how the contact pairs stack up for each event:
| Number of People | Contact Pairs | Risk Compared to 10 People |
|---|---|---|
| 10 | 45 | – |
| 50 | 1225 | 27x |
| 100 | 4950 | 110x |
Currently, the R value for COVID-19 in the U.S. is around 1-2, meaning one infected person typically spreads the virus to 1-2 others. However, this is an average figure, and a single superspreader event can infect dozens or even hundreds of people at once. Not only does the sheer number of contact pairs increase, but the likelihood of encountering a superspreader also rises. When a superspreader is present and there are more contact pairs, things can escalate rapidly. Clearly, eight people aren’t just four times riskier than two—they’re significantly more dangerous.
Quadratic risks have limits, but they're incredibly high. Entire nations have seen dramatic shifts in outbreak patterns due to isolated superspreader incidents, like the football match in Milan or the South Korean church cluster—and right now, the Beijing seafood market. So, hosting a small dinner party once a week is likely far safer than attending a massive, crowded gathering—even just once. A community might face greater overall risk from a single large event than from numerous small group interactions over time. The risk is quadratic, not linear.
... While Other Risks Increase Exponentially
Imagine you're presymptomatic with COVID-19 and contagious for a week. During that time, you attend several small dinner parties with ten people each. How many people could potentially be exposed in the week following your contagious period, before you even realize you’re sick?
This number doesn’t grow linearly with the number of events attended. Instead, it skyrockets exponentially. If you and nine friends attend just one dinner party and stay home otherwise, you’re relatively safe—only nine additional people have been exposed. But if everyone attends two events, the situation changes dramatically. Suppose each attendee from your first dinner party joins another one. At those second dinners, the attendees from your original group could encounter nine more people. By the time everyone has attended just two gatherings, a hundred people are involved.
Here comes the exponential twist: if everyone at your initial dinner party then goes to two additional events, and the people at those events attend yet more small gatherings, you’ll soon have a thousand people in the chain. Before you even realize you’re sick, you’ve inadvertently exposed a thousand people. Thus, staying in smaller groups is safer, but limiting your social interactions and sticking with the same people is even better. Constantly mingling with new groups increases the risk of accidental spread exponentially.
The Bottom Line: Understanding Dynamics Is Key
Reopening isn’t an all-or-nothing decision. Once we’re open, there are countless ways to minimize our own risks and protect loved ones. We don’t have a fixed limit on how much we can reopen. The unique math of viral spread means some activities—and specific ways of conducting them—are vastly more dangerous than others. With this knowledge, communities can adopt many low-risk behaviors with less danger than a few high-risk activities. As a result, we can maintain an R value below 1 while opening up significantly more. Low-risk actions can outweigh even small amounts of high-risk behavior.
For more insights into managing COVID-19 risks:
- Doctors Rank Activities by COVID-19 Risk
- State of the Pandemic, June 2020, Part I: What We Know About SARS-CoV-2
- How to Assess Your Personal Risk Factors for Severe Illness if Infected
- The CDC’s Reopening Plan Was Set Aside, But It Still Offers Guidance
- Fact-Checking the CDC’s New Advice: You Should Still Disinfect Packages [Updated]
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