Chaos, Percolation and the Coronavirus Spread: the Italian case

Abstract

A model based on chaotic maps and turbulent flows is applied to the spread of Coronavirus for each Italian region in order to obtain useful information and help to contrast it. We divide the regions into different risk categories and discuss anomalies. The worst cases are confined between the Appenine and the Alps mountain ranges but the situation seem to improve closer to the sea. The Veneto region gave the most efficient response so far and some of their resources could be diverted to other regions, in particular more tests to the Lombardia, Liguria, Piemonte, Marche and V. Aosta regions, which seem to be worst affected. We noticed worrying anomalies in the Lazio, Campania and Sicilia regions to be monitored. We stress that the number of fatalities we predicted on March 12 has been confirmed daily by the bulletins. This suggests a change of strategy in order to reduce such number maybe moving the weaker population (and negative to the virus test) to beach resorts, which should be empty presently. The ratio deceased/positives on April 4, 2020 is 5.4% worldwide, 12.3% in Italy, 1.4% in Germany, 2.7% in the USA, 10.3% in the UK and 4.1% in China. These large fluctuations should be investigated starting from the Italian regions, which show similar large fluctuations.

Chaos, Percolation and the Coronavirus Spread

“…Thus, in order to have some sensitivity from this analysis, we need to have a constant number of tests performed every day, otherwise it is better to study the ratio of the number of positives divided the total number of tests as we discuss below. For the case of Figure 3, we expect that increasing the number of tests daily of more than a factor of 3 will increase the number of positives accordingly [6]. The Japanese case is very interesting since it seems to be spreading very slowly (small Lyapunov exponent).…”

“…The Japan case is not close to the saturation value, thus we had to force d ∞ to a finite value to perform the fit. the virus and we will discuss it in more detail for the Italian case where such information was available at the time of writing to the public [6].…”

“…A large number of the deceased had other serious conditions, however, data on the age and physical conditions of the tested/deceased are not given. A more detailed study of the Italian case is in progress [6].…”

“…This percolation mechanism might be at this point out of control and maybe a strategy would be to search for negatives (especially older people) and move them away from higher risk places. At the time of writing it seems that the spreading is contained below the Appenine mountains, which seem a natural division of the northern part (the Po valley-the most affected), from Tuscany and the center part of Italy [6].…”

“…We also suggest that a highly dense population is a principal cause to "feed" the virus. High densities imply a large number of cases, which might overcome the capabilities of health facilities, thus producing a large number of fatalities and substantial differences among different countries having more resources (for instance, ventilators) [6]. Moving higher risk populations to lower densities might help to limit the impact of the virus.…”