I have spent significant part of this summer reading papers on the modeling of COVID-19. It helped a lot that majority of them were quite terrible, those have saved me some time. Though there were also a few more interesting ones. In  it was shown that the distribution of deaths and cases over US counties follows a power-law distribution. This finding is quite similar to Zipf's law, but specifically for the epidemic spread.
In this post we will replicate the empirical finding and in the next post we will consider a theoretical model to explain such observation.
To verify the results presented in  we have used publicly available data available at https://github.com/CSSEGISandData/COVID-19. To be exact, we are using CSSE time series files for confirmed cases and deaths in the US. We have downloaded the data on August 5th, 2020.
In the interactive app below you can select specific date, \( t \). The app will plot the probability density function of confirmed cases, \( I \), (blue curve) and deaths, \( D \), (red curve). Note that samples, or random variates, here are case and death counts of each county at specific \( t \).
Note that such approach is somewhat similar to the compartmental voter model I have written a lot before the summer holidays.
- K. Burghardt, K. Lerman. Unequal Impact and Spatial Aggregation Distort COVID-19 Growth Rates. arXiv:2004.12994 [q-bio.QM].