Why socially isolate? And what follows?

A chart is making the rounds: isolate to spread out pandemic progression, allow the health system to cope, in particular to take care of the ~15% of those infected who need it.

That's true, but what's the end game? Are we to isolate for ever? No. Spreading out the curve is only part of the story.

There's a magic number, called R0, which is the average number of others a single patient infects (if they're not already immune).

If R0 were below 1, the disease would clearly die out. If R0 is a big number, infections grow rapidly.

R0 for coronavirus seems to presently be at least 2.2, some sources say 2.5. That's higher than the common flu, which is 1.3. 

R0 is related to another magical number, called the herd immunity threshold (HIT). That's the proportion of immune individuals needed in the population for disease to not persist. 

It's typically used to calculate what proportion of the population needs to be vaccinated to stop a disease from becoming an epidemic. So e.g. measles, rubella, chickenpox/smallpox etc have super-high R0 of 10 or more, which translates to a HIT of 90% or more. (The relationship is actually a pretty simple formula, HIT=1-1/R0) That's why we need near-universal vaccination to control or eradicate those diseases. But HIT is also the fraction of the population that will get infected (and hence immunized) in the absence of other sources of immunity. With coronavirus' current R0, HIT is around 55-60%. If R0 stays around 2.2-2.5, that's the portion of the population that will get it. (Of which, currently 15% will have a hard time and a couple % will not make it.)

Social isolation done well will temporarily reduce R0, since the viruses won't be able to jump to as many new hosts. Apart from allowing the system to cope better (and take care of the more seriously ill in particular), it buys time for a more permanent reduction in R0. Better hygiene, such as hand washing, will lower R0 for as long as people remember to do it. Better testing, identification and therefore targeted isolation/treatment of those infected will reduce R0 in a sustainable manner. Better understanding of the virus will clarify what are its most effective transmission pathways. Combined, this will permit relaxing crude mechanisms like broad social isolation, allowing the broader non-infected and recovered-and-immune population to return back to more normal life (hopefully having learned better hygiene, and maybe also that less CO2-spewing travel is absolutely necessary!) Finally, a vaccine, if one is ready in a year or so, might not affect R0 itself but will helicopter us closer to the HIT without suffering illness (providing -- hopefully -- immunity from vaccine or having recovered from illness is reasonably long-lasting).

In math (calculus) speak, yes we're spreading out the curve but we're also buying time to reduce the total area under the curve (which is essentially the HIT, or HIT multiplied by the population to be precise). If we socially isolate AND reduce R0, this smaller area under the curve will allow us to relax crude-but-currently-necessary precautions sooner.

Appendix added later:

People have why the formula linking R0 and HIT is what it is. Here is a simple explanation. Suppose p is the portion of the population not yet immune/infected. The viruses from a given infected individual will on average attempt to "take over" R0 individuals as the "next generation" virus factory. They will on average be successful in p R0 (the 2 numbers multiplied) cases. The infection rate will continue to increase provided p R0 > 1, the 1 being what it takes to replace the infected individual themselves as they (hopefully) recover. This is equivalent to p > 1/R0. Finally, the HIT is precisely 1 minus (or 100% minus) the critical level of p. Therefore 1-HIT=1/R0 or equivalently HIT=1-1/R0.

All of this a bit simplified; in particular it assumes infected and recovered individuals have a reasonable level of immunity. And that the death rate is small enough it can be ignored in this mathematical calculation. Let's hope...

[I'm not a virologist or public health professional. But my work - risk and strategy under uncertainty - involves drawing conclusions from math and communicating about it. This is an attempt to combine various information floating around into a simple narrative. Corrections and sharing welcome. Originally posted March 14 to facebook; to LinkedIn on March 15; minor edits March 16]