To see the impact of Extreme Measures, look at R0

Its been a week for many of us since social distancing has closed schools, events, and many businesses.  In my last post, I explained how the current growth is about discovering cases that existed before these measures were taken. Even if nobody in the US caught COVID (and I'm sure many did) since last Monday we would still see the new cases spiking because of the amount of tests were now doing (up again by a almost 50K on a Sunday!)

So how will we see the effect of these measures and what are they likely to be?  To start with this question, you have to learn about how a figure Epidemiologists use to measure and predict the growth of a pandemic.  R0 (called "R naught") is the measure of the number of people someone with a virus will infect on average during the time they are contagious.  There's a lot of intense math involved in calculating this number, but if you knew R0, you would expect the number of cases in the future to be   Present Cases x R0 ^ Generations (^ means "to the power of") .  Generations is the time for someone infected to become contagious themselves.  The math to measure R0 based on actual data can be very complicated and can vary widely.  Fortunately, all you have to know for this post is that R0 has three inputs:

• The average number of people in a day exposed to someone who is contagious
• The average probability someone exposed to a contagious person will be infected themselves
• The number of days someone is contagious

R0 is these three factors multiplied together.  We can guess at these numbers, and large numbers of researchers around the world are working to discover them for COVID, but to know the impact of a preventative measure on R0, we just have to know we've reduced one of these factors.  

If we estimate that on average the number of people someone in the US is exposed to in a day has dropped by 75%, then R0 has also dropped by 75%.  To see the difference, let's look at the current number of confirmed active cases in the US and how the cases grow using an R0 with no measures and one with social distancing:

If you factor in people who are recovering from COVID, the red line should turn downwards relatively soon while the blue line would continue to move up.  Remember that we're seeing growth from cases before social distancing -- ones where people had symptoms and others where it could take 7-14 days to show up -- so we'll still see that growth.  It normally takes around 5 days for a test to even show positive once someone is infected, so the effect of the last week will only start having an effect now.  The real fruit of those efforts will take a while longer to show up on reports.

 Social distancing isn't the only thing that has probably changed R0 in the last week.  The factor for the number of days someone is contagious speaks to the number of days they are spreading the virus.  Hopefully, most people running the typical starting symptoms -- low fever, cough, running nose -- isolated themselves very early compared to a few weeks ago when it would be typical to assume its just a cold and continue mingling with the public.  The 14 days that typically figures into R0 for someone spreading their germs is probably only a few days now.  That's another big R0 discount. 

The third factor is the probability someone exposed catches the virus. Washing hands regularly and staying away from common areas where you may come in contact with droplets left behind from someone with the virus should reduce this probability.  There's also a plausible reason to believe that warmer weather reduces the amount of time the virus can survive in droplets and on surfaces, so warmer weather could reduce this factor all by itself.  

Public health workers see R0 as a threshold.  When its higher than 1, people are infected at a higher rate than they recover and get off the roles so the number grows rapidly.  When R0 is less than 1, you have more people recovering than are replaced by new infections and the number of active cases shrinks rapidly.   Estimates for R0 in the US are around 2.0,  so if the steps taken last week reduce it by 50% or more, it could have a major effect on on the peak number of cases in the US.  This view was echoed in the highly respected medical journal The Lancet in an article from March 9th  (back when we only had 700 cases and we still had sports).

Social distancing measures reduce the value of the effective reproduction number R. With an early epidemic value of R0 of 2·5, social distancing would have to reduce transmission by about 60% or less, if the intrinsic transmission potential declines in the warm summer months in the northern hemisphere. This reduction is a big ask, but it did happen in China. 

As we all know,  the Lancet got their "Big Ask" and we went to extreme measures to reduce transmission.  

Of course there will be some people who don't reduce their social connections, don't quarantine themselves when they have COVID symptoms, and aren't taking more care to wash their hands and take other common sense measures,  for R0, is only matters what has changed on average.  Specific cases either way aren't enough to change R0.

The bottom line is that if you think we've cut in half any combination of the number of contacts on average people have with each other, the number of days on average someone contagious is out in the public before self quarantine, and the chance a virus particle makes it into your body, then you have good reason to expect to see improvement as the reports continue.