COVID-19 risks aren't straightforward—they're far more complex than simply doubling when you add more people. For instance, four people dining together isn’t just twice as risky as two—it’s three times riskier. This is something many of us tend to overlook, especially since so many of us try to avoid revisiting those dreaded high school math lessons. But grasping concepts like network effects and the differences between linear, quadratic, and exponential relationships can help you make smarter decisions about risk management as life begins to reopen, and unfortunately, as some people take unnecessary chances.
Just because you've already taken some risks—like going to the grocery store—doesn’t mean you should abandon all caution. Most of us recognize that our risks exist on a spectrum. Even at crowded events, wearing a mask and washing your hands remains crucial. Similarly, eating outdoors is generally safer than dining indoors in a poorly ventilated space.
However, the nuances of these risk spectrums often remain unclear to the public. People tend to oversimplify situations, thinking, "Maybe attending two events is only twice as risky as going to one?" But that's not how it works due to the nonlinear nature of COVID-19 transmission.
More: Contrary to what some claim, the WHO never stated that asymptomatic individuals couldn't spread the virus.
Some Risks Are Quadratic…
Let’s look at three events with the same conditions, except for the number of attendees: 10, 50, and 100 people. When two people interact—even if it's just passing by—they form what’s called a "contact pair." These contact pairs represent opportunities for the virus to spread. The total number of contact pairs grows roughly according to the square of the number of people present. Here’s how the contact pairs stack up:
| Number of People | Contact Pairs | Risk Compared to 10 People |
|---|---|---|
| 10 | 45 | – |
| 50 | 1,225 | 27x |
| 100 | 4,950 | 110x |
The current R value for COVID-19 in the U.S. hovers around 1-2, meaning one infected person typically spreads the virus to 1-2 others. However, this is an average figure, and certain "superspreader" events can infect many more 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 in a large group, things can escalate rapidly. Even if math isn’t your strong suit, it’s clear that eight people aren’t merely four times riskier than two—they’re significantly more dangerous.
Quadratic risks have limits, but they’re incredibly high. Entire nations have experienced dramatic shifts in outbreak patterns due to isolated superspreader events, such as the Milan football match or the South Korean church incident, and currently, the Beijing fish market. Therefore, hosting a few friends over for dinner weekly is likely safer than attending a massive, crowded party—even once. A community might face greater overall risk from one large gathering than from numerous small, intimate gatherings over time. The risks compound quadratically, not linearly.
Other Risks Increase Exponentially
Imagine you contract COVID-19 but are presymptomatic and contagious for a week. During that time—when you unknowingly spread the virus—you attend several events, each with 10 people.
These events’ attendees will likely go to other gatherings. How extensive is the contact chain after a week of contagiousness but before you realize you’re ill?
This number doesn’t grow linearly with the number of events people attend—it skyrockets exponentially. If you and nine friends go to just one dinner party and stay home the rest of the time, you’re relatively safe. All ten of you will have come into contact with nine others, totaling 90 interactions.
But if everyone attends two events, the math flips. Suppose each person from your dinner party goes to a second gathering. At those other dinners, the people from your group could interact with nine additional individuals. After just two gatherings per person, the chain involves 100 people.
Ready for more exponential growth? If everyone at your dinner party then goes to two other dinner parties, and the attendees at those parties mingle with others, you’ll suddenly involve 1,000 people in the chain. Before you even realize you have COVID-19, you’ve unintentionally exposed 1,000 people.
Thus, staying in smaller groups is safer, but you’re even better off limiting your social interactions and consistently meeting the same people instead of different ones each time. If you meet new people every week and those individuals also mingle with others, the risk of accidental spread grows exponentially fast.
The Bottom Line: Understanding Dynamics Is Key
Reopening isn’t a binary decision—either fully open or fully shut down. Once reopened, we have countless options to mitigate our risks and those of loved ones. Our "budget" of opening isn’t fixed either. The unique math of viral spread means some activities—and specific ways of engaging in them—are dramatically riskier than others.
By comprehending and leveraging these dynamics, communities can implement a wide range of low-risk behaviors with less danger than even a small amount of high-risk activities. As a result, we can maintain control over the spread (R-value under 1) while opening up significantly more.
Explore more of our coverage on 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 Risk Factors for Severe Illness if You Contract 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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