The effect of quarantine on the spread of coronavirus

The R0 of a virus is the number of people each person infects, assuming the whole population is susceptible (i.e. no herd immunity).  It's not a fixed number for each virus, as it depends not only on how inherently contagious the virus is, but also on the behavior of the population in question.  You will therefore see ranges rather than fixed numbers for R0.  Social distancing is an attempt to bring down the R0, so is the wearing of masks.  If you can get the R0 down below 1, the virus will die out, as there are not enough new cases to replace the old ones. 

Highly infectious viruses with high R0 values include measles (12-18) and chickenpox (5-10).  Flu is much lower, in the range 1-2.5. 

R0 estimates for the new coronavirus vary widely, with the most commonly reported range 2-3.  But in the case of the Diamond Princess cruise ship, we have a worst-case scenario of crowding.  Interestingly, the R0 value increases over time from the 2-3 range to as high as 11.  The latter high number appears to have happened after the implementation of quarantine of passengers to their individual rooms.  Couples and families were then stuck together in a small space, giving it to each other.  But once everyone who was going to get it had gotten it, the rate of spread dropped.

In this graph, the vertical dashed line is the beginning of the quarantine to individual rooms.  The horizontal dashed line is the reproduction number of 1, the point where spread will die out.

Source here

Note that five days after the ship's version of social distancing was implemented, transmission had dropped dramatically.  And by 10 days after, transmission had dropped below 1.

If we look instead at the graph of daily new cases, a number we're getting from various countries in quarantine now, we see an initial increase over a few days, followed by a slow decline. 

Italy, by comparison, looks like this, with the vertical line placed on 3/18, the point where my one FB friend in Italy tells me that they really started tightening down movement in public.

The good news is that Italy has had two consecutive days of decline.  Yes, I know the data aren't perfect; it could be under-testing.  But it could also be the beginning of the end, paralleling the decline on the Diamond Princess.  The bad news is that the decline in new cases was pretty slow on the ship. 

France has technically been on lockdown since 3/17, a week ago.  But the French are not exactly rule-followers, and there were initially several days where the police were first giving out a small fine, then a larger one. But people are even now still reporting that they are seeing some groups of people still gathering on the street, against the rules.  Every day the rules get tightened a little more.  I'm going with 3/19 as the point where people started to take it seriously, although there is some wiggle room there.

I will definitely be watching France over the next few days.