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 a quantitative analysis of the regrowth 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 Singapore, France, Spain and Italy are analyzed.
During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such behaviour has been obtained from 2020 late spring data coming from China by Ziff and Ziff in Ref. [1]. After this important observation the power-law scaling (albeit with different exponents) has also been observed in other countries during periods of containment of the spread. Early interpretations of these results suggest that this phenomenon might be due to spa…
Resource support between individuals is of particular importance in controlling or mitigating epidemic spreading, especially during pandemics. Whereas there remains the question of how we can protect ourselves from being infected while helping others by donating resources in fighting against the epidemic. To answer the question, we propose a novel resource allocation model by considering the awareness of self-protection of individuals. In the model, a tuning parameter is introduced to quantify the reaction strength of individuals when they are aware of the disease. And then, a coupled model of…
Here, we focus on the data analysis of the growth of epidemic spread of Covid-19 in countries where different policies of containment were activated. It is known that the growth of pandemic spread at its threshold is exponential, but it is not known how to quantify the success of different containment policies. We identify that a successful approach gives an arrested phase regime following the Ostwald growth, where, over the course of time, one phase transforms into another metastable phase with a similar free energy as observed in oxygen interstitial diffusion in quantum complex matter and in…
We propose an epidemiological model that includes the mobility patterns of the individuals, in the spirit to those considered in (Barmak, 2011, 2016) and (Medus, 2011). We assume that people move around in a city of 120x120 blocks with 300 inhabitants in each block. The mobility pattern is associated to a complex network in which nodes represent blocks while the links represent the traveling path of the individuals. We implemented three confinement strategies in order to mitigate the disease spreading: 1) global confinement, 2) partial restriction to mobility, and 3) localized confinement. In …
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 spreadin…
As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on the COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well wit…
The Covid-19 epidemic of the novel coronavirus (severe acute respiratory syndrome SARS - CoV-2) has been spreading around the world. While different containment policies using non-pharmaceutical interventions have been applied, their efficiency are not known quantitatively. We show that the doubling time Td(t) with the success s factor, the characteristic time of the exponential growth of Td(t) in the arrested regime, is a reliable tool for early predictions of epidemic spread time evolution and it provides a quantitative measure of the success of different containment measures. The efficiency…
So far most of the analysis of coronavirus 2020 epidemic data has been focusing on a short-time window and consequently a quantitative test of statistical physical laws of Coronavirus Epidemics with Containment Measures (CEwCM) is currently lacking. Here we report a quantitative analysis of CEwCM over 230 days, covering the full-time lapse of the first epidemic wave. We use a 3D phase diagram tracking the simultaneous evolution of the doubling time Td(t) and reproductive number Rt(t) showing that this expanded parameter space is needed for biological physics of CEwCP. We have verified that in …
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures (CSRwCM) there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the dynamics of the Covid-19 dynamics Italy and its administrative Regions. The supercr…
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in…
COVID-19 has spread from China across Europe and the United States and has become a global pandemic. In countries of the Global South, due to often weaker socioeconomic options and health care systems, effective local countermeasures remain debated. We combine large-scale socioeconomic and traffic survey data with detailed agent-based simulations of local transportation to analyze COVID-19 spreading in a regional model for the Nelson Mandela Bay Municipality in South Africa under a range of countermeasure scenarios. The simulations indicate that any realistic containment strategy, including th…
Assessing the risk of epidemic spread on networks and developing strategies for its containment is of tremendous practical importance, both due to direct effects in public health and its impact on economies. In this work we present the numerical results of a stochastic, event-driven, hierarchical agent-based model designed to reproduce the infectious dynamics of the cattle disease called Bovine Viral Diarrhea (BVD), for which the corresponding network of movements is the main route of spreading. For the farm-node dynamics, the model takes into account a vast number of breeding, infectious and …
Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit express…
Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution …
The special epistemic characteristics of the COVID-19, such as the long incubation period and the infection through asymptomatic cases, put severe challenge to the containment of its outbreak. By the end of March 2020, China has successfully controlled the within-spreading of COVID-19 at a high cost of locking down most of its major cities, including the epicenter, Wuhan. Since the low accuracy of outbreak data before the mid of Feb. 2020 forms a major technical concern on those studies based on statistic inference from the early outbreak. We apply the supervised learning techniques to identif…
We propose a novel testing and containment strategy in order to contain the spread of SARS-CoV2 while permitting large parts of the population to resume social and economic activity. Our approach recognises the fact that testing capacities are severely constrained in many countries. In this setting, we show that finding the best way to utilise this limited number of tests during a pandemic can be formulated concisely as an allocation problem. Our problem formulation takes into account the heterogeneity of the population and uses pooled testing to identify and isolate individuals while prioriti…
Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which is still hardly been clarified. Methodology/Principal Findings: In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time bef…
The recent outbreak of a novel coronavirus and its rapid spread underlines the importance of understanding human mobility. Enclosed spaces, such as public transport vehicles (e.g. buses and trains), offer a suitable environment for infections to spread widely and quickly. Investigating the movement patterns and the physical encounters of individuals on public transit systems is thus critical to understand the drivers of infectious disease outbreaks. For instance previous work has explored the impact of recurring patterns inherent in human mobility on disease spread, but has not considered othe…
While understanding of periodic recurrent waves of Covid-19 epidemics would aid to combat the pandemics, quantitative analysis of data over a two years period from the outbreak, is lacking. The complexity of Covid-19 recurrent waves is related with the concurrent role of i) the containment measures enforced to mitigate the epidemics spreading ii) the rate of viral gene mutations, and iii) the variable immune response of the host implemented by vaccination. This work focuses on the effect of massive vaccination and gene variants on the recurrent waves in a representative case of countries enfor…
Since the outbreak of COVID-19, many data analyses have been done. Some of them are based on the classical epidemiological approach that assumes an exponential growth, but a few studies report that a power-law scaling may provide a better fit to the currently available data. Hereby, we examine the data in China (01/20/2020--02/24/2020), and indeed find that the growth closely follows a power-law kinetics over a significantly wide time period. The exponents are $2.48(20)$, $2.21(6)$ and $4.26(12)$ for the number of confirmed infections, deaths and cured cases, respectively, indicating an underl…
We consider the pandemic spreading of COVID-19 in India after the outbreak of the coronavirus in Wuhan city, China. We estimate the transmission rate of the initial infecting individuals of COVID-19 in India by using the officially reported data at the early stage of the epidemic with the help of Susceptible (S), Exposed (E), Infected (I), and Removed (R) population model, the so-called SEIR dynamical model. Numerical analysis and model verification are performed to calibrate the system parameters with official public information about the number of people infected, and then to evaluate severa…
In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks, and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural cha…
Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We quantitatively document four phases of the outbreak in C…
The spread of COVID-19 during the initial phase of the first half of 2020 was curtailed to a larger or lesser extent through measures of social distancing imposed by most countries. In this work, we link directly, through machine learning techniques, infection data at a country level to a single number that signifies social distancing effectiveness. We assume that the standard SIR model gives a reasonable description of the dynamics of spreading, and thus the social distancing aspect can be modeled through time-dependent infection rates that are imposed externally. We use an exponential ansatz…
