The novel coronavirus COVID-19 epidemic is currently leveling off in China but on the upswing in the rest of the world. Understanding and modeling this growth is obviously of high importance. We noticed that for several weeks, the number of deaths in China could be fit by a power law with exponent of about 2.25, suggesting a kind of fractal or small-world behavior going on. Traditional epidemiological models, such as the Susceptible-Exposed-Infected-Recovered models (SEIR) puts groups in compartments and use differential equations to predict the behavior, but there is no spatial or network properties taken into account. At early times, the growth is exponential depending upon the reproduction rate, and for later times those models predict an s-shaped curve. The power-law result predicted a greater growth of the epidemic than many people were predicting. More recently, the daily deaths in China have dropped off exponentially, in fact following a model of A. Vazquez from 2006. At the same time, the growth in the number of total deaths in other parts of the world is tracking the behavior in China, delayed by one month. The small-world, fractal idea suggested that this world-wide transmission was likely to take place, and the belief that it could be contained in China was clearly short-sighted.

Reference: A. L. Ziff and R. M. Ziff, medrXiv 2020 submitted.