Chaos, Percolation and the Coronavirus Spread
A. Bonasera, Suyalatu Zhang
Abstract
The dynamics of the spreading of the COVID-19 virus has similar features to the turbulent flow, chaotic maps and other non-linear systems: a small seed is implanted, it grows exponentially and eventually saturates. Like in the percolation model, the virus is mostly 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>1000 persons/km2). A ‘seed’ implanted in such towns 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 S.Korea, Italy and China respectively. The best approach to contrast the virus once it became out of control, might be to move the weaker population to lower density regions, for instance summer resorts near the sea.