I'm trying to wrap my head around some of the information I'm reading about how to fight Covid-19 and conflicting opinions about how much "social distancing" is required to avert a disaster, or whether social distancing works at all. (I am a data scientist, not a biologist or medical professional)

First I want to check if some of my assumptions are correct or not:

  1. Flattening the curve doesn't reduce the overall number of infections, only the average rate of infection for a given time period, e.g. Flattening the curve doesn't take you from 1000 infected people to 100 infected people, it takes you from 1000 infected people in a week to 1000 infected people in 3 months (numbers are just examples): True or False?
  2. The purpose of social distancing is to flatten the curve, not to reduce the number of overall cases: True or False?
  3. If $r_0 > 1$ than growth is exponential: True or false?
  4. Sub-exponential growth can only happen if $r_0 \leq 1$: True or false?
  5. Flattening the curve cannot reduce exponential growth in number of cases to sub exponential growth, it only leads from steep exponential growth, e.g. $r_0 \approx 2.5$ or $r_0 \approx 3$, to "not so steep" exponential growth $r_0 \approx 1.5$ or $r_0 \approx 1.2$: True or False?

Assuming 1-5 are correct, here are the more complex questions I am trying to figure out:

  • Can social distancing (without hard quarantines, tracking as many cases as possible, and instantly isolating any new cases discovered, etc...) actually lead to $r_0 < 1$ and therefore reduce the number of infections as opposed to just spreading them out to a manageable rate?

  • I think the answer is "No", because of small world network theory: The majority of people respect prefect social distancing, i.e. they maintain zero social contact with anybody outside of their immediate family and the the people they interact with for procuring life essentials. Because the number of people who cannot practice social distancing due to their essential role in society (grocery and pharmacy employees, health care professionals, law enforcement, etc...) will still experience very high transmission rates, a small world phenomenon occurs, where the average chain of transmission is still very short between any two individuals in an impacted area. What is wrong with this line of reasoning?

  • In general, is $r_0 < 1$ achievable without a cure, a vaccine, herd immunity, or the ability to track infections with very high accuracy and isolating them instantly?
  • $\begingroup$ SE Biology is a question and answer site — not a discussion site or a site for floating ideas. It is concerned with the mechanisms of biological processes, not medical or social aspects of biology. For one of these reasons I think that your question on the coronavirus outbreak is off-topic here. Question of a medical nature might be on-topic at SE Medical Sciences. Otherwise you are advised to consult more appropriate reputable sources for such information, some of which are listed here. $\endgroup$ – David Mar 22 '20 at 10:33
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    $\begingroup$ @David why are epidemiology and coronavirus tags that are available for posts then, if this question is not appropriate for this SE? $\endgroup$ – Skander H. Mar 22 '20 at 19:01
  • $\begingroup$ @SkanderH. Tags have nothing whatsoever to do with what is on or off topic. Anyone can create a tag. What is on topic here is defined in the Tour and the Help. I am on my phone so cannot immediately give you links to these, but I imagine you are smart enough to find them yourself. Please do. $\endgroup$ – David Mar 22 '20 at 19:21

I believe r0 is an exponent...

It is the average number of individuals who become infected by each infected individual.

If one infected individual infects exactly one other individual (r0 = 1), the progress will be straight line; the rate will be a flat line based on "mean time between infections"; total number of infections over time will be linear sloping upwards.

If r0 > 1, then it will be an exponential increase; how rapidly/steeply it curves up depends again on the mean time over which that propagation of infection occurs.

If r0 < 1, then it will be an exponential decay. New infections continue to occur, but the overall rate of infection decreases toward but never quite reaching zero.


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