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

We discuss a two-step model for the rise and decay of a new coronavirus (Severe Acute Respiratory Syndrome-CoV-2) first reported in December 2019, COVID-19. The first stage is well described by the same equation for turbulent flows, population growth and chaotic maps: a small number of infected, d 0 , grows exponentially to a saturation value, d ∞ . The typical growth time (aggressive spreading of the virus) is given by τ = 1 λ where λ is the Lyapunov exponent. After a time t crit determined by social distancing and/or other measures, the spread decreases exponentially analogous to nuclear decays and non-chaotic maps. Some countries, like China, S. Korea and Italy, are in this second stage while others including the USA are near the end of the growth stage. The model predicted 15,000 (±2250) casualties for the Lombardy region (Italy) at the end of the spreading around May 10, 2020. Without the quarantine, the casualties would have been more than 50,000, one hundred days after the start of the pandemic. The data from the 50 US states are of very poor quality because of an extremely late and confused response to the pandemic, resulting unfortunately in a large number of casualties, more than 70,000 on May 6, 2020, and more than 170,000 on August 21, 2020. S. Korea, notwithstanding the high population density ( 511 / km 2 ) and the closeness to China, responded best to the pandemic with 255 deceased as of May 6, 2020, and 301 on August 21, 2020.

The coronavirus spread: the Italian case.

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.

Mapping heart dynamics by using nonlinear indicators.

A novel approach for the nonlinear characterization of Electrocardiogram (ECG) signals has been developed. The new developed methodology is based on a numerical algorithm that extracts the value of dinfinity (d-infinite) characterizing the asymptotic chaotic behavior of a system. This algorithm also extracts a measure of the maximum Lyapunov exponent and it is applicable to time series where the knowledge of the system structure and laws is not necessary. In order to prove the significance of the extracted parameters, the presented algorithm was applied on a statistically significant number of ECG signals taken from the MIT-BIH database and including normal subjects and subjects affected by arrhythmia and ventricular arrhythmia. A systematic study, analyzing how dinfinity varies with initial condition was performed showing the sensitivity of such parameter to the initial conditions. Furthermore, two maps, one presenting the maximum Lyapunov exponent and the other the dinfinity versus a control parameter II, as a measure of the rate variation, were drawn using the parameters extracted by the experimental data. They clearly show three distinguishable zones where the normal subjects and the subjects affected by the two different pathologies can be mapped and discriminated. Concluding, the newly presented algorithm, thanks to its implementation features and its effectiveness, it lends itself to future real-time implementation for clinical application in the early diagnosis of cardiac pathologies.

Chaos driven fusion enhancement factor at astrophysical energies.

We perform molecular dynamics simulations of screening by bound target electrons in low energy nuclear reactions. Quantum effects corresponding to the Pauli and Heisenberg principles are enforced by constraints. We show that the enhancement of the average cross section and of its variance is due to the perturbations induced by the electrons. This gives a correlation between the maximum amplitudes of the internuclear oscillational motion and the enhancement factor. It suggests that the chaotic behavior of the electronic motion affects the magnitude of the enhancement factor.