# Why Social Distancing Works

Even if a certain percentage of the population is infected.

The US (and indeed almost every country in the world) is now infected with COVID19. Given that we are (somewhat) infected should we simply “give up”, and “take the hit” aka “develop herd immunity”?

The answer is absolutely NO. Here’s why

# A very simple model.

According to the latest stats, 3,774 people in the US have been diagnosed with COVID 19. Accounting for the fact that many still don’t show symptoms, that many mild cases may be unreported, and that tests are still unavailable in mass, we can estimate the true number of infected at between 100,000 people and 1 million people. For argument sake, let’s assume 300,000 people, or 0.1% of the US population.

So we can think of this as

Group A: (the infected) 300,000 people

Group B: (the non-infected) 300 Million people.

Each member of group A spreads it to 20% new members of group B every day, dragging them into Group A. This daily contagion stat is *in line* with the Death Rate Math observed here. The net effect is the contagion spreads very, very quickly hitting millions in April.

# Now assume that we are 80% socially distant

We now have 4 groups:

Group A1: (the infected who quarantine): 240,000 people

Group A2: (the infected who do not quarantine): 60,000 people

Group B1: (the non-infected who quarantine): 240 Million people

Group B2: (the non-infected who do not quarantine): 60 Million people.

Now the only spreading can happen between group A2 and Group B2. In the earlier model we had a 20% contagion ration from A to B. But now, 80% of the old contagions for group A2 no longer occur (as 80% of B quarantine), and on top of it, A2 starts in a smaller base (60K vs 240K).

I would argue the correct model is now to use a 4% contagion rate (20%*20%) instead of 20%. The difference is 3x over 1 month vs 237x over 1 month.

Proof: (1.04)³⁰ = 3 while (1.2)³⁰=237.

On top of this, you have the lower base. So you would get the following if the quarantine started tomorrow

No quarantine: 300,000 * 237 = 71 million infected (70.7 Million new)

Quarantine: 240,000 + 60,000*3 = 420,000 infected (120,000 new)

obviously you buy *a lot of time*.