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://www.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.

Linear systems behave nicely - whenever you slightly increase the input, the output also increases only by a small amount. Thus linear systems are quite easy to predict. You can make small errors in measurements of your inputs, which will have almost no impact on the accuracy of your prediction.

Nonlinear systems are different in this regard - even small difference in the input can lead to divergent outputs. In other words the differences between the systems trajectories, or alternatively differences between your prediction and the actual behavior of the system, won't be noticeable at first, but with time those small differences will get amplified. Typical example being weather, where tomorrows forecast are likely to be more reliable than 7-day forecast.

More nonlinear systems, dynamical chaos and chaos theory in the following video by Seeker. We invite you to watch it.

Today we continue our series of posts on compartmental voter model. Recently I had another idea how to examine the impact of the finite capacity on the compartmental voter model dynamics. And this approach also involves populations dynamics in the model.

For a different approach see the earlier post on the finite capacity in the compartmental voter model.