How Many Social Distancing Scofflaws is Too Many?

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When I’ve been outside recently, I see a most people respecting the social distancing guidelines. Unfortunately I also see a few people being lax about either wearing a mask or keeping their distance or both. I wondered

  • Are these people just endangering themselves?

  • Should I be angry at them for not considering the health of their community?

  • How many people would it take to ruin it for our healthcare workers?

Being the data scientist that I am I thought I would use a simple model to help me think about this question. I took the very simply modified SIR model from a different page of this site, Insight: Flattening, and ran it with different numbers which I describe below. I based my numbers on Santa Clara county because they’re the county that’s providing me with the most detailed reports, Bay Area Dashboard Rankings.

In this simple model Santa Clara’s ICUs are overloaded for 60 days and 750 people die if just 10% of Santa Clara’s population is lax about flattening the curve.

In this simple model Santa Clara’s ICUs barely escape being overloaded if just 3.75% of Santa Clara’s population is lax about flattening the curve.

Think about what this means for the healthcare workers of Santa Clara. If just a small portion of the population doesn’t respect the shelter in place order, then Santa Clara’s emergency departments could be profoundly affected. A small subset of people through their negligence may be deciding whether healthcare workers themselves get sick because of overloaded hospitals.

Consider your Community’s Vulnerable Population

I’ve described the people violating the shelter in place orders as scofflaws, but these could also be our vulnerable population who have a much harder time sheltering in place than those of us who are privileged. If you care about nothing else except the medical professionals who will treat you when you get sick, you must still do the compassionate thing and look to help those less fortunate shelter in place effectively. Helping those less fortunate helps keep our healthcare system from being overly impacted.


Caveat: This is a very simple model that is only here to capture the rough order of magnitude of this effect. These numbers do not reflect what is likely to happen especially because the facts on the ground may change significantly.


The Model Basics

I changed a very simple SIR (Susceptible Infected Recovered) model of this epidemic to include the following assumptions.

  • 98.8% of the people who are infected need no additional care and recover on their own.

  • The remaining 1.2% of infections need ICU care but eventually all those patients, if they have an ICU bed, recover on their own too. This 1.2% is a very low conservative number.

  • The only time people die in this simulation is when there aren’t enough ICU beds to go around. In that case I declare that anyone without an ICU bed dies.

  • I assume 161 ICU beds for a population of 2 million. This is what was available on April 10th.


Model Inputs: Population and Days to Double

Conceptually I split the population of Santa Clara into two groups. In the larger population social isolation was perfect and there was no spread of COVID-19 through this large population. In the small sub-population social isolation was being practiced but it wasn’t being practiced diligently. The days to double for this smaller population was 5. This rate is a bit slower than the days to double that I was seeing in the Bay Area before shelter in place took effect.

I ran the simulation once using the susceptible population set to 200,000 which is roughly 10% of Santa Clara’s population. I ran the simulation a second time to find the largest population that just grazed the ICU capacity but didn’t go over. That population turned out to be about 75,000 or roughly 3.75% of Santa Clara’s population.

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