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The fractal time growth of COVID-19 pandemic: an accurate self-similar model, and urgent conclusions

Current available data of the worldwide impact of the COVID-19 pandemic has been analyzed using dimensional analysis and self-similarity hypotheses. We show that the time series of infected population and deaths of the most impacted and unprepared countries exhibits an asymptotic power law behavior, compatible with the propagation of a signal in a fractal network. We propose a model which predicts an asymptotically self-similar expansion of deaths in time before containment, and the final death toll under total containment measures, as a function of the delay in taking those measures after the expansion is observed. The physics of the model resembles the expansion of a flame in a homogeneous domain with a fractal dimension 3.75. After containment measures are taken, the natural fractal structure of the network is drastically altered and a secondary evolution is observed. This evolution, akin to the homogeneous combustion in a static isolated enclosure with a final quenching, has a characteristic time of 20.1 days, according to available data of the pandemic behavior in China. The proposed model is remarkably consistent with available data, which supports the simplifying hypotheses made in the model. A universal formulation for a quarantine as a function of that delay is also proposed.

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