I’m not a doctor (not in medicine, anyway) but I am something of a specialist in probability and statistics. These are my thoughts on a low-probability, high-impact event: COVID-19 infection.

Let’s start with historical data, but the important idea is that historical statistics are predictors of the past, not the future. They are based on a state of the universe that existed some time before the statistics were taken, and the universe has changed – a lot – since then. The numbers behind the statistics are growing, and the thing that matters – and we don’t know – is the growth rate of those numbers.

Consider the population people already infected with COVID-19 (as we will in a couple of paragraphs). That number is changing all the time.

Popular media like to use the term “exponential growth” to mean something like “a lot”, but that’s not the point. If the growth rate is near zero, than it takes a very long time for the population to increase even with exponential growth. If the growth rate is high, then the population is increasing in size rapidly.

What is the risk of contracting COVID-19 in New Mexico based on historical statistics? How does it compare to neighboring Western states? If we assume completely random interactions across the whole state, here is the probability of exposure **per interaction with another person** based on infection rates on the morning of 15 March 2020

NM | 0.00000621 |

OR | 0.00000835 |

WA | 0.00008055 |

CA | 0.00000956 |

ID | 0.00000114 |

UT | 0.00000285 |

CO | 0.00001791 |

AZ | 0.00000167 |

Those are really small numbers, and kind of hard to visualize. What’s the biggest crowd I anticipate encountering? Less than 10,000 – I hope! So, in a crowd of 10,000, how many would be infected?

NM: less than two-thirds of a person

OR: slightly more than four-fifths of a person

WA: slightly more than eight people

CA: slightly less than one person

ID: slightly more than one-tenth of a person

UT: slightly more than one-fourth of a person

CO: a little less than two people

AZ: slightly more than one-sixth of a person

What we don’t know is the probability of infection given exposure, which is certainly less than 1.0. Worse case, assume 1.0, so these are also the risks of infection.

In reality, the probability of encountering the infection is much, much higher. Testing is only done on a very small fraction of individuals with symptoms, so there’s a lot more infected people out there. And an unknown number of carriers are asymptomatic.

So what if the probability were ten times greater? Reduce the size of the crowd above to 1,000. Here in NM, if you want a better than 50/50 chance of avoiding infection, avoid crowds of 500 or more.

But these are all probabilities – your mileage will vary. You could meet only one person in a day but it could be the wrong person.

To reduce your exposure, stay home. When you do go out, avoid crowds. Even little crowds.

Assume you are exposed when you go out. These are ways to reduce your probability of infection:

- DON’T TOUCH YOUR FACE
- Wash your hands when you get home.
- Disinfect your cellphone
**before**you wash your hands (you’re likely to have handled your cellphone while you were in a higher-risk environment like the supermarket). Don’t touch the disinfected phone before you wash your hands. - Avoid crowds and, more importantly, close proximity to others. Self-check-out at the supermarket looks better, doesn’t it? Not so much because there’s no checker opposite the register, but there’s no one standing right behind you in line, at least while you’re scanning.
- Ordering online looks even better, no? DISINFECT ANY PACKAGES YOU RECEIVE. That package has been a lot of places and handled by a lot of people.