Chaos, Percolation and the Coronavirus Spread

Abstract

The dynamics of the spreading of the COVID-19 virus has similar features to turbulent flow, chaotic maps, and other non-linear systems: a small seed grows exponentially and eventually saturates. Like in the percolation model, the virus is most dangerous if the probability of transmission (or the bond probability p in the percolation model) is high. This suggests a relation with the population density, ρs, which must be higher than a certain value (ρs > 1,000 persons/km2). A “seed' implanted in such populations grows vigorously and affects nearby places at distance x. Thus, the spreading is governed by the ratio ρ = ρs/x. Assuming a power law dependence τ of the number of positives to the virus N+ from ρ, we find τ = 0.55, 0.75, and 0.96 for South Korea, Italy, and China, respectively.