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, ρ s , which must be higher than a certain value (ρ s > 1,000 persons/km 2). A "seed' implanted in such populations grows vigorously and affects nearby places at distance x. Thus, the spreading is governed by the ratio ρ = ρ s /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.

Chaos, Percolation and the Coronavirus Spread: a two-step model

“…For the Italian case, the first test was published on February 24 and equation (1) was fitted on March 10 before the quarantine was announced, i.e. March 14 [7]. The plateau was reached around March 24 as predicted by the model.…”

“…Chaotic models have been successfully applied to a large variety of phenomena in physics, economics, medicine and other fields [1][2][3][4][5][6]. In recent papers [7,8] a model based on turbulent flows and chaotic maps has been applied to the spread of COVID-19 [9]. The model has successfully predicted the rise and saturation of the spreading in terms of probabilities, i.e.…”

Chaos, percolation and the coronavirus spread: a two-step model

“…Chaotic models have been successfully applied to a large variety of phenomena in physics, economics, medicine and other fields [1][2][3][4][5][6][7]. In recent papers [8,9], a model based on turbulent flows and chaotic maps has been applied to the spread of COVID-19 [10,11]. The model has successfully predicted the rise and saturation of the spreading in terms of probabilities, i.e., the number of infected (or deceased) persons divided by the total number of tests performed.…”

“…The model has successfully predicted the rise and saturation of the spreading in terms of probabilities, i.e., the number of infected (or deceased) persons divided by the total number of tests performed. Also a dependence on the number of cases on the population density has been suggested [8], and the different number of fatalities recorded in different countries (or regions of the same country) was attributed to facilities overcrowding [9]. In this paper, we would like to extend the model to the second stage, i.e., the decrease in the number of events due to quarantine or other measures [12].…”

“…Different fitting parameters of the model are due to the different actions, a e-mail: zhengh@snnu.edu.cn (corresponding author) 0123456789(). : V,-vol social behaviors [13], population densities [8], pollution [14], etc., of each country, but there are some features in common, and it is opportune to first have a look at some data available on May 6 which we updated to the end of June and to the middle of August, 2020 when available.…”