In this post we present a theoretical explanation for the power-law distributions observed in the spatial growth of COVID-19. From theoretical point-of-view it is interesting why power-law distribution is observed in the data, as typical epidemic spread is characterized by an exponential distribution (at least the SIR model predicts this). Yet, the explanation is pretty simple and is based on the Reed-Hughes mechanism [1].

I would like to share another fine visual simulation of epidemic spread created by Primer, which was sent to me by a student (thanks for the link!). It is extremely visually appealing, so we invite you to watch it!

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 [1] 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.

We have talked a lot about the opinion dynamics recently, thus before going on summer holiday, we would like to share a very relevant post by a computational linguist K. Simler. In the said post he explores the complexity of social systems from the point of view of various network topologies on which a diffusion process (which can be either contagion or idea and information spread) plays out. This tutorial also involves a lot of neat interactive apps.

We encourage you to explore "Going critical" on https://meltingasphalt.com/interactive/going-critical/.

See you after the summer holidays!

We are concluding the ongoing series of posts on the compartmental voter model. As in [1] we will conclude with comparing the model against UK census data. Though note that the interactive app does not allow for the comparison - it just allows to generate semi-realistic spatial rank-size distributions.