So You’re Going Outside: A Physics-Based Coronavirus Infection Risk Estimator for Leaving the House

So we’re quarantined. We’re social distancing, avoiding groups, and staying 6 feet apart as much as possible. But this still leaves so many questions!

  • What if the sidewalk is only 4 feet wide — should I #stayHomeSaveLives?
  • How does “riskiness of the hangout” scale with “length of the hangout”?
  • How risky is going to Costco vs. going to the corner store?
  • How does this all change if we’re wearing masks?

I’m a mathematician, and I’m quarantined in a community house with nine other people. Burning questions like this came up at all our meetings, so to sync our collective understandings, I made a physics-based activity risk model and fed our questions into it.

In the rest of this article, I’ll step through the answers, and I’ll show you how to use the model to answer questions of your own!

Disclaimer: all models are wrong, but some are useful. I think this one is useful, but please bear in mind that I made it in a week. The exact percentages are definitely inaccurate. I’m sharing because I think the general, directional trend information it reveals — distinguishing between a 1% risk and a 10% risk — is much better than no information at all.

The Model

How to Use It

Here’s the link to download my Jupyter notebook on GitHub. And, here’s a link to a Google spreadsheet version, if you prefer that format. The parameters are documented in the code — change them to match your scenario!


Many specifics of coronavirus transmission are still being debated, so I kept my math at a high level. I considered three widely-agreed-upon kinds of transmission:

  1. Surface-based: you touch an object that has virus on it, then touch your face.
  2. Warm-body-based: you come near a living, breathing infected person, and viral particles from their breathing then infect you in a diffusion-based way.
  3. Wildcard: a catch-all for everything else that’s beyond the scope of this model. Fluid dynamics of airborne particles are weird enough that this term is definitely nonzero, though it’s hard to say exactly how big it is. Probably small?

Many pencils and pieces of paper later (check out my full handwritten derivation if you want to know how many), here are the summary equations! I explain the parameters in more detail in the code and spreadsheet, and show them for the calculated examples.


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