COVID-19 Case Dynamics  

18 Day Phase Space Dynamics



A plot of the COVID phase space dynamics for the U.S.
      Per capita COVID cases are increasing - increasing phase - in the upper part of the plot (above zero on the left axis). 
      Per capita COVID cases are decreasing - decreasing phase - in the lower part of the plot (below zero on the left axis). 
      The horizontal axis is per capita number of new cases (per 100,000 population) and the vertical axis is daily change in 
      per capita cases. The daily change is negative for the lower part of the plot and positive for the upper part.

Home     Seven Day Phase Dynamics Plots



The plot above shows the COVID-19 18-day case growth rate dynamics computed from The New York Times, based on reports from state and local health agencies[1].

Per capita COVID cases are increasing - increasing phase - in the upper part of the plot (above zero on the left axis). Per capita COVID cases are decreasing - decreasing phase - in the lower part of the plot (below zero on the left axis).

The number of new COVID-19 cases each day varies for multiple reasons. One is that states have varying ways of reporting new COVID-19 cases, and in some cases there are very regular fluctuations: daily, weekly, maybe monthly. These fluctuations are addressed by taking a moving average over some number of days (18 days unless the plot says otherwise).

Another dynamic that appears is the actual long run increase in the number of cases per capita (seen between early March and late March in the plot above, or from March to July 2020 in the plot below) or decrease in the number of cases per capita (during May below or following mid January 2021 in the plot near the bottom of this page). The other dynamic is fluctuations due to short variations in exposure and infection, and these appear to have periods of around a week even after smoothing. Falling case numbers seem to have stalled in March 2021. This is discussed in some detail - along with contributions for individual states - at the bottom of this page.

[1]The New York Times. (2020). Coronavirus (Covid-19) Data in the United States. https://github.com/nytimes/covid-19-data

A plot of the COVID phase space dynamics for the U.S. from March to July in 2020.

In the absence of any long run change, the phase plot would make a circle of sorts - called an orbit - about a point along the zero-daily-change line. This is clearly evident in the small orbits in April and June in the plot above. The April orbit is centered about 8.9 cases per 100,000 while the June orbit is centered about 6.6 cases per 100,000. Orbits like these occur occasionally in the national plots and more frequently in individual state plots.

The rest of the dynamics - the looping U shapes in the lower half and the inverted U shapes in the upper half - represent natural oscillations in new COVID-19 cases superimposed on a long run trend. The distance of these U shapes from the zero line is a measure of how far the system is from stable oscillations. Moving oscillations are a bad thing when cases are increasing, as in the upper part of the plot, but a good thing when cases are decreasing, as in the lower part of the plot.

Aside from the decrease in cases during May, the overall trend in the plot above is an increase from zero to 20.0 cases per 100,000 on 31 July 2020. The dip between 26 and 28 July 2020, centered at 19.6 cases per 100,000, suggests a coming change in case dynamics.

A plot of the COVID phase space dynamics for the U.S. from July to October in 2020.

Evident in the plot above is that the July dip was a prelude to a fall throughout August from 19.8 to 13.1 cases per 100,000. The drop stalled in September with month-long orbit-like dynamics (Big September orbit) about a mean of 12.1 cases per 100,000. There appears to be an actual orbit on the low side (Little September orbit) about a mean of 11.6 cases per 100,000. The September stall is followed by rapid increase in cases throughout October from 12.9 to 21.6 cases per 100,000, more than erasing all of the improvement in August.

A plot of the COVID phase space dynamics for the U.S. from July to October in 2020.

The steady growth in new cases throughout October led into the holiday surges following Hallowe'en, Thanksgiving, and the Christmas / New Year holidays (see the Holiday Surges page). The surge following Hallowe'en took new cases from 27.1 to 50.6 cases per 100,000. The Thanksgiving surge saw an additional increase to 65.3 cases per 100,000. The Thanksgiving surge was followed by a brief recovery with new cases falling from 65.3 down to 60.1 cases per 100,000.

A plot of the COVID phase space dynamics for the U.S. from July to October in 2020.

The post-Thanksgiving recovery was followed by the Christmas and New Year surge that took new cases from 60.3 to the record national rate of 71.1 cases per 100,000. The Christmas / New Year surge was followed by a long period of falling case rates as seen in the plot at the top of this page. The Christmas / New Year surge ended on 16 January 2021 and was followed by a continuous dramatic drop to 20 new cases per 100,000 in early March, shown in the plot below. The tight orbits in March are shown in detail in the plot at the top of this page.

A plot of the COVID phase space dynamics for the U.S. from July to October in 2020.

The phase dynamics of the whole pandemic are shown in the following plot.

A plot of the COVID phase space dynamics for all States plus District of Columbia, Guam, Northern Mariana Islands, Puerto Rico, and Virgin Islands.
      Per capita COVID cases are increasing - increasing phase - in the upper upper part of the plot (above zero on the left axis). Per capita COVID cases are 
      decreasing - decreasing phase - in the lower part of the plot (below zero on the left axis). The horizontal axis is per capita number of cases (per 100,000 
      population) and the vertical axis is daily change in per capita cases. The daily change is negative for the lower part of the plot and positive for the upper
      part.

State Phase Dynamics Plots

The March Stall

Following the 16 Jan 2021 maximum of 71.1 cases per 100,000, the number of new cases fell rapidly and continuously until 3 March 2021. The decrease stalled briefly in early march with an orbit about 19.7 cases per 100,000, then fell slightly to stall again for the remainder of March with an orbit about 17.6 cases per 100,000. The March stall brings the number of new cases down to the level in late July 2020. The March stall takes three general forms in the state plots:

Note that Guam, Northern Mariana Islands, and U.S. Virgin Islands are not included in this list. The numbers of cases are so low that dynamic analysis may not be meaningful. Cases per 100,000 in Hawai'i are also so low that dynamic analysis may not be meaningful there, either.