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.