What's troubling about the classical logistic equation formulation with the herd immunity inflection point and asymptotic leveling off is that it requires a significant proportion of the population to kick in -- since the negative feedback is a (1-*N/population*) factor where *N* is number infected. British PM Boris Johnson and his chief scientific adviser got into hot water for [suggesting that herd immunity on the scale of 40 million people (60% of population) infected as the leveling-off mechanism which will ultimately keep it under control](https://www.ft.com/content/38a81588-6508-11ea-b3f3-fe4680ea68b5) (inflected=infected as a mnenomic).
So is herd immunity an oxymoron in this case? It appears that **avoiding** a herd of people is what's keeping the pandemic under control at the moment in places like China and South Korea. The classic logistic contagion model dictates that the disease stops spreading after enough people are infected, but what happens if re-infections are possible? -- as [reports from China and now Japan indicate that re-infection is occurring](https://thehill.com/changing-america/well-being/prevention-cures/484942-japan-confirms-first-case-of-person-reinfected) (also found multiple opinions such as *"there is no herd immunity if re-infection is possible"* a la possible mutations and potential vaccine ineffectiveness)
Take a look at comment #11 above and you can see how the stochastic dispersive model takes into account sub-populations that individually reach an asymptote and that these can be superposed to create an inflection point at much less than 60% of the total population. Isolation of these sub-populations is the key factor to model the growth in China. The bigger question is whether this can continue until a vaccine is developed. Keep our fingers crossed.
From Twitter :
> "I am deeply uncomfortable with the message that UK is actively pursuing ‘herd immunity’ as the main COVID-19 strategy. Our group’s scenario modelling has focused on reducing two main things: peak healthcare demand and deaths..."
Consider dominos as a propagating contagion. A break in the dominos limits the propagation but occasionally one can slip through. That's the importance of strict quarantining.
Subvolume and social distancing simulations in the WaPo