Social distancing

Officials across the country have ordered assemblies of varying sizes to not meet. Here in San Antonio, the mayor ordered assemblies of 500 or more to not meet, with exemptions for schools and churches. My church regularly has beween 700 and 900 congregants, and Friday night the elders scrapped Sunday service. It was a wise decision.

As of this morning, American coronavirus casualties numbered 93 deaths out of 4,748 cases, a mortality rate of almost 2%. I coded a simulator to predict the infection rates and mortality rates for large gatherings, assuming 100% transmission. Here are my findings:

Groups of 25

Chance of outbreak: .0126%

Groups of 50

Chance of outbreak: .0462%

Groups of 100

Chance of outbreak: .1288%

Groups of 250

Chance of outbreak: .3492%

Groups of 500

Chance of outbreak: .7136%

Groups of 1,000

Chance of outbreak: 1.4364%

You'll notice that, for large groups of people, the second-most likely outcome after no virus transmission is a high number of deaths. Imagine walking into a worship hall of 500 people knowing there was a .7% chance there will be an outbreak. Furthermore, if there was an outbreak, it was 3 times as likely to kill 10 people than 5. Would you still go to church, or would you stay home?

These are the numbers officials are looking at. And, since I'm assuming total randomness in the distribution of infected, it's going to look worse in areas like Washington state, where there is a high concentration of cases.

The simple fact of the matter is, if you have the virus and don't know it, you're going to kill 2 percent of the people you come into contact with. And since you can go days without showing symptoms, avoiding large groups of people is simply the prudent thing to do.

Now that the country is on alert, I predict in the next week the growth curve for the number of cases will invert, while deaths will rise disproportionately to case growth. The final mortality rate will settle in between 2% and 3%.

As always, let me know what you think in the comments. I'll reply to you as soon as I can. If you're looking for something to do while social distancing, I invite you to read the first 4 chapters of my new book, Seeds of Calamity, for free. If it piques your interest, get yourself a copy at Amazon. I appreciate the support!

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UPDATE: In the time it took to write this, the number of coronavirus cases rose to 5,243, and deaths rose to 94. Get the live numbers here.

UPDATE 2 (3/18):I found a flaw in my predictive model. The number of coronavirus cases that we know of does not reflect the true number of people carrying the virus. Since we are still seeing exponential growth in the number of new cases (1,748 just yesterday, up from 983 on Monday), it's safe to assume there are tens of thousands of people carrying the virus who don't know it. That drastically increases the risk of assembling in large groups.

So I ran the simulation again using the current mortality rate of 1.588%. Instead of looking at the probability for each possible outcome, I devised a new metric that averages potential mortality rates. Here are the results:

	# of infected in general population
Group size	10,000	20,000	30,000
25	.00033	.00059	.00093
50	.0013	.0025	.0036
100	.0048	.0096	.014
250	.030	.060	.090
500	.12	.24	.35
1000	.47	.93	1.4

Notice the linear growth in mortality as the number of infected increases, contra the exponential growth in mortality as the group size increases. Limiting group size is an effective way to limit the virus's mortality.

Assuming 30,000 people in the general population are infected, the expected mortality in a gathering of 1,000 people is 1.4. It seems low because 91% of those gatherings won't experience an outbreak (assuming a random distribution of infected people). The 9% that do, however, will probably see between 8 and 24 deaths. Of course, an outbreak among a church or school body of 1,000 people means you have 1,000 new carriers of the virus who won't show symptoms for 2 to 14 days.

That's another part of what makes the coronavirus frightening. It's why I think it'll be 2 weeks from March 13, the day we basically went on high alert, before we see the growth in the number of new cases start to taper.

UPDATE 3 (3/19):I'm learning more about the coronavirus every day, and I'm becoming more ashamed of my willful ignorance in the lead up to last week.

This morning I ran an exponential regression on the last 3 weeks of diagnosed cases in America. The equation it spat out has an r value of .995, which in statistics is as close to a guarantee as it gets. If we use the equation as a predictive model, there will be 93,610 cases by March 27, at which point I think the number of daily new cases will start to decline. That means there are over 80,000 undiagnosed cases currently in the general population. So the 10,000 to 30,000 cases in the general population I simulated yesterday paints too rosy a picture.

So I ran the simulation again with more realistic infected numbers and the current mortality rate.

Expected mortality and outbreak probability
	# of infected in general population
Group size	60,000		80,000		100,000
25	.0018	.15%	.0025	.21%	.0031	.26%
50	.0075	.51%	.0099	.68%	.012	.82%
100	.029	1.5%	.039	1.9%	.049	2.4%
250	.18	4.4%	.24	5.7%	.30	7.2%
500	.71	8.7%	.94	11%	1.2	14%
1000	2.7	17%	3.5	22%	4.3	26%

Look at those outbreak probabilities! How can you not cut out restaurants, the gym, church, school, and office buildings? Isolate yourself now, especially from older folks whose mortality is an order of magnitude higher than the average.

UPDATE 4 (July 2021): Suffice to say my sense of danger from COVID-19 has changed since last spring. I panicked and advocated for radical measures based on incomplete and incorrect information. I apologize for my naiveté and credulity.