COVID Day 50 New Cases Data

COVID-19 Death Rates

A basic characteristic of epidemics is that, until a significant percentage of the population is infected, the number of infected persons is an exponential function of time, N(t)=N0 2^{t/d}, where d is the doubling time and N0 is the initial population. In order to slow down the rate of infections, it is desirable to make d as large as possible by, for example, social distancing as we are currently doing in the COVID-19 pandemic.

      To monitor progress in social distancing, one can monitor the fractional daily increase in the number of cases \Delta ln(N) =\Delta N/N, from which the doubling time becomes d=ln(2)/\Delta ln(N).  Because the daily numbers fluctuate, the fractional daily increases are noisy and it is convenient to average a few days together to see what the trends are. Here are recent US COVID data plotted this way:

The data clearly show that, since serious distancing began being practiced in mid-March, the doubling times have greatly increased.  Equivalently, the daily percentage increases have fallen substantially.

     The total cases data are always suspect due to testing problems.  Data on deaths should be more reliable  (though not infallible as some people, particularly in NYC, have chosen to die uncounted at home.  This should not be a large fraction of the totals, though.) What is encouraging is that the daily deaths data are also showing substantial decreases in the percentages as a function of time, again starting in late March.

Rather than increasing exponentially, the death rates have been quite steady at about 2,000/day.  Again, this suggests that the social distancing efforts implemented in most of the states are effective and managing to keep our death rates at a manageable level (NYC being the notable exception).  Had the death rates continued to climb at 25% per day, as they were doing in late March,  the death rates would be over 5000/day on April 10.

The Science-free Eclipse

Note (March 2020).  This post was composed in 2018, but never posted.  But I still agree with it, so better now than never!

A little confession to start this post.  I've hated virtually every planetarium show I've ever attended.  What?  Why would a science type hate a planetarium show?  Because they typically spend 90% of the time talking about constellations.  There is no science in constellations!  The operator goes into great detail identifying the constellations, naming the various stars and drawing lines between them to show the bear or whatever.  Content free.  The big exception was the night an amateur astronomer friend of mine put on a planetarium show for our Cub Scout troop.  He quickly went through the requisite constellation stuff, then showed us photographs he had taken of the rings of Saturn.  In addition to the spectacular photos, he explained how he took them, and described many features I had never known about.  I enjoyed that immensely.

The recent eclipse mania was, alas, reduced to a outside planetarium show.  As an example, check out CNN's "The Solar Eclipse, in Pictures".  It is mostly pictures of people viewing the eclipse!  There is a nice picture of the corona, which can only be seen by eye during an eclipse, without even mentioning it.

In the various discussions of the eclipse, if anything scientific is discussed, it is an explanation of why eclipses happen so rarely.  That's great, I like that.  But what is rarely discussed is that the eclipse is only possible due to the nearly identical angular sizes of the moon and sun.  And what is the nature of that corona?  What do we know about the fields and charged particles that are only so rarely revealed to the naked eye?  How do scientists learn about them without waiting for rare eclipses?  The soul hungering for some science starves with the media coverage of this supposedly scientifically important event!

COVID-19 Progress

A look at the COVID data: Here is the March US data of daily new cases. It is better to look at that data rather than the total number of cases because the daily number tells you how you are doing now, information that takes a while to show up in the totals. Furthermore, the plot is on a logarithmic scale. On such a scale, exponential growth shows up as a straight line. The slope of the line tells the doubling time for new cases, how long it takes for the number of daily cases to double.

You can see that from March 1 to about March 21 the US new cases followed the straight line very well, with a doubling time of about 2.3 days. However, my daughter and I noticed early this week that that the new cases were now doubling only every 5-6 days. This is significant; today the US had about 19,000 new cases but if we had continued on last week's curve there would have been 73,000 new cases today! I think this is encouraging news. We're still on an apocalyptic trend, but it will take us twice as long to get there now!

Data from worldometers.info, updated April 3, 2020.