  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.
