ABSTRACT
In all countries the political decisions aim to achieve an almost stable configuration with a small number of new infected individuals per day due to Covid-19. When such a condition is reached, the containment effort is usually reduced in favor of a gradual reopening of the social life and of the various economical sectors. However, in this new phase, the infection spread restarts and, moreover, possible mutations of the virus give rise to a large specific growth rate of the infected people. Therefore, a quantitative analysis of the regrowth pattern is very useful. We discuss a macroscopic approach which, on the basis of the collected data in the first lockdown, after few days from the beginning of the new phase, outlines different scenarios of the Covid-19 diffusion for longer time. The purpose of this paper is a demonstration-of-concept: one takes simple growth models, considers the available data and shows how the future trend of the spread can be obtained. The method applies a time dependent carrying capacity, analogously to many macroscopic growth laws in biology, economics and population dynamics. The illustrative cases of France, Italy and United Kingdom are analyzed.
ABSTRACT
A comparative analysis of the COVID-19 diffusion in North African countries, Algeria, Egypt, Morocco and Tunisia has been carried out with the aim to study the effects of the containment efforts in different nations and the reliability of the predictions based on the data fits by macroscopicgrowth laws with a small number of free parameters. The comparison with data shows that the Coronavirus spreading has often different phases: an initial exponential behavior, followed by a Gompertz one and/or by a logistic phase, due to containment effort. The study of the growth phases permits to verify the restarting of the disease spreading after a stationarity period due to new outbreaks or to the weakness of the social control measures. The response of the National Health Systems to the emergency is discussed and some short-term predictions on the cumulative number of confirmed infected, on the hospitalizations and on the total number of deaths is done. The possible correlation with immigration in other Mediterranean Countries has been analyzed. Stable (or unstable) conditionof the spreading can quickly change due to a stronger or weaker application of the lockdown measuresand short-term predictions turn out to be reliable. © 2021 World Scientific Publishing Company.
ABSTRACT
Macroscopic growth laws describe in an effective way the underlying complex dynamics of the spreading of infections, as in the case of Covid-19, where the counting of the cumulative number N(t) of detected infected individuals is a generally accepted variable to understand the epidemic phase. However, N(t) does not take into account the unknown number of asymptomatic cases A(t). The considered model of Covid-19 spreading is based on a system of coupled differential equations, which include the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution has been compared with N(t), determined by a single differential equation with no explicit reference to A(t), showing the equivalence of the two methods. The model is applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for N(t) has been observed in more recent data. The information contained in the time series N(t) turns out to be reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.
ABSTRACT
To evaluate the effectiveness of the containment on the epidemic spreading of the new Coronavirus disease 2019, we carry on an analysis of the time evolution of the infection in a selected number of different Countries, by considering well-known macroscopic growth laws, the Gompertz law, and the logistic law. We also propose here a generalization of Gompertz law. Our data analysis permits an evaluation of the maximum number of infected individuals. The daily data must be compared with the obtained fits, to verify if the spreading is under control. From our analysis, it appears that the spreading reached saturation in China, due to the strong containment policy of the national government. In Singapore a large growth rate, recently observed, suggests the start of a new strong spreading. For South Korea and Italy, instead, the next data on new infections will be crucial to understand if the saturation will be reached for lower or higher numbers of infected individuals.