The coronavirus spread: the Italian case

Abstract

A model based on population growth, 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: a two-step model

“…We have discussed and applied the first stage of the model in Refs. [8,9]. We briefly recall it and write the number of people (or the probability) positive to the virus (or deceased for the same reason) as [1,2,4-9,15]:…”

“…1 and 2, but in reality it should be applied not to the number of positives (or deceased) but to their probabilities, i.e., the number of cases divided by the total number of tests. The main reason for this definition is to avoid the spurious time dependence due to the total number of tests, which varies on a daily basis and very often not in a smooth way [8,9]. In Fig.…”

“…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].…”

“…This defines the probability to be infected or the death rate probability due to the virus. We stress that such probability may be biased since often the number of tests is small and administered to people who are hospitalized or show strong signs of the virus [8,9]. The values we will derive must be considered as upper limits, but the time evolution should be realistic.…”