Power-law distribution in the number of confirmed COVID-19 cases

Nonlinear shifts and dislocations in financial market structure and composition

This paper develops new mathematical techniques to identify temporal shifts among a collection of US equities partitioned into a new and more detailed set of market sectors. Although conceptually related, our three analyses reveal distinct insights about financial markets, with meaningful implications for investment managers. First, we explore a variety of methods to identify nonlinear shifts in a market sector structure and describe the mathematical connection between the measure used and the captured phenomena. Second, we study a network structure with respect to our new market sectors and identify meaningfully connected sector-to-sector mappings. Finally, we conduct a series of sampling experiments over different sample spaces and contrast the distribution of Sharpe ratios produced by long-only, long-short, and short-only investment portfolios. In addition, we examine the sector composition of the top-performing portfolios for each of these portfolio styles. In practice, the methods proposed in this paper could be used to identify regime shifts, optimally structured portfolios, and better communities of equities.

Beyond scale-free networks: integrating multilayer social networks with molecular clusters in the local spread of COVID-19

This study evaluates the scale-free network assumption commonly used in COVID-19 epidemiology, using empirical social network data from SARS-CoV-2 Delta variant molecular local clusters in Houston, Texas. We constructed genome-informed social networks from contact and co-residence data, tested them for scale-free power-law distributions that imply highly connected hubs, and compared them to alternative models (exponential, log-normal, power-law with exponential cutoff, and Weibull) that suggest more evenly distributed network connections. Although the power-law model failed the goodness of fit test, after incorporating social network ties, the power-law model was at least as good as, if not better than, the alternatives, implying the presence of both hub and non-hub mechanisms in local SARS-CoV-2 transmission. These findings enhance our understanding of the complex social interactions that drive SARS-CoV-2 transmission, thereby informing more effective public health interventions.

Heavy-tailed distributions of confirmed COVID-19 cases and deaths in spatiotemporal space

This paper conducts a systematic statistical analysis of the characteristics of the geographical empirical distributions for the numbers of both cumulative and daily confirmed COVID-19 cases and deaths at county, city, and state levels over a time span from January 2020 to June 2022. The mathematical heavy-tailed distributions can be used for fitting the empirical distributions observed in different temporal stages and geographical scales. The estimations of the shape parameter of the tail distributions using the Generalized Pareto Distribution also support the observations of the heavy-tailed distributions. According to the characteristics of the heavy-tailed distributions, the evolution course of the geographical empirical distributions can be divided into three distinct phases, namely the power-law phase, the lognormal phase I, and the lognormal phase II. These three phases could serve as an indicator of the severity degree of the COVID-19 pandemic within an area. The empirical results suggest important intrinsic dynamics of a human infectious virus spread in the human interconnected physical complex network. The findings extend previous empirical studies and could provide more strict constraints for current mathematical and physical modeling studies, such as the SIR model and its variants based on the theory of complex networks.

Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies

Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as an increase in the market's collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a "best value" portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better-established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market and to what extent. The results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies.

Power law in a bounded range: Estimating the lower and upper bounds from sample data

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and, in many cases, also an upper bound. Estimating these bounds from sample data is notoriously difficult, with a recent method involving O(N3) operations, where N denotes sample size. Here I develop an approach for estimating the lower and upper bounds that involve O(N) operations. The approach centers on calculating the mean values, x̂min and x̂max, of the smallest x and the largest x in N-point samples. A fit of x̂min or x̂max as a function of N yields the estimate for the lower or upper bound. Application to synthetic data demonstrates the accuracy and reliability of this approach.

What is the optimal country for minimum COVID-19 morbidity and mortality rates?

The SARS-CoV-2 is a deceptive virus. Despite the remarkable progress in genetic sequencing and subsequent vaccine development, the world continues to grapple with the ominous threats of rapidly appearing SARS-CoV-2 variants. The objective of this manuscript is to rank world countries based on the anticipated scope of COVID-19 morbidity and mortality, measured in terms of prevalence per 1 million persons, from the lowest to the highest. The ranking of 162 countries is based on predictions of empirical models, which include three explanatory variables: hospital beds per thousand persons, population density, and the median age of the country's population. Referring to the COVID-19 scope of morbidity, the lowest likelihood of infection is obtained in Niger and Mali, where the dominant characteristic is the young median age (15.1-16.4 years). Referring to the COVID-19 scope of mortality, the lowest likelihood is obtained in Singapore. For Singapore, the dominant feature is the high population density. The optimal solution is intensive vaccination campaigns in the initial phase of the pandemic, particularly among countries with low GDP per capita. Yet, vaccinations may work only where the personal immune system is healthy and thus respond by creating antibodies to the SARS-CoV2 virus. Referring to populations that lack the natural protection of the healthy immune system and thus cannot be vaccinated (e.g., old people, cancer patients undergoing chemotherapy treatments), a complementary solution might be coordination between countries and the establishment of field hospitals, testing laboratories, isolation of areas, humanitarian aid-in the same manner of treatment in other disasters like earthquakes.

Distributional Trends in the Generation and End-Use Sector of Low-Carbon Hydrogen Plants

This paper uses established and recently introduced methods from the applied mathematics and statistics literature to study trends in the end-use sector and the capacity of low-carbon hydrogen projects in recent and upcoming decades. First, we examine distributions in plants over time for various end-use sectors and classify them according to metric discrepancy, observing clear similarity across all industry sectors. Next, we compare the distribution of usage sectors between different continents and examine the changes in sector distribution over time. Finally, we judiciously apply several regression models to analyse the association between various predictors and the capacity of global hydrogen projects. Across our experiments, we see a welcome exponential growth in the capacity of zero-carbon hydrogen plants and significant growth of new and planned hydrogen plants in the 2020’s across every sector.

A coalitional game-based joint monitoring mechanism for combating COVID-19

In the absence of effective treatment for COVID-19, disease prevention and control have become a top priority across the world. However, the general lack of effective cooperation between communities makes it difficult to suppress the community spread of the global pandemic; hence repeated outbreaks of COVID-19 have become the norm. To address this problem, this paper considers community cooperation in disease monitoring and designs a joint epidemic monitoring mechanism, in which adjacent communities cooperate to enhance their monitoring capability. In this work, we formulate the epidemiological monitoring process as a coalitional game. Then, we propose a Shapley value-based payoffs distribution scheme for the coalitional game. A comprehensive analytical framework is developed to evaluate the advantages and sustainability of the cooperation between communities. Experimental results show that the proposed mechanism performs much better than the conventional non-cooperative monitoring design and can greatly increase each community's payoffs.

Power Law for Estimating Underdetection of Foodborne Disease Outbreaks, United States

We fit a power law distribution to US foodborne disease outbreaks to assess underdetection and underreporting. We predicted that 788 fewer than expected small outbreaks were identified annually during 1998-2017 and 365 fewer during 2018-2019, after whole-genome sequencing was implemented. Power law can help assess effectiveness of public health interventions.

The distribution of COVID-19 mortality

We estimate the distribution of COVID-19 mortality (measured as daily deaths) from the start of the pandemic until July 31st, 2022, for six European countries and the USA. We use the Pareto, the stretched exponential, the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions. The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data. We also compute Value-at-Risk measures as well as mortality probabilities with our estimates. We also discuss the implications of our results and findings from the point of view of public health planning and modelling.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

It is well established that COVID-19 incidence data follows some power law growth pattern. Therefore, it is natural to believe that the COVID-19 transmission process follows some power law. However, we found no existing model on COVID-19 with a power law effect only in the disease transmission process. Inevitably, it is not clear how this power law effect in disease transmission can influence multiple COVID-19 waves in a location. In this context, we developed a completely new COVID-19 model where a force of infection function in disease transmission follows some power law. Furthermore, different realistic epidemiological scenarios like imperfect social distancing among home-quarantined individuals, disease awareness, vaccination, treatment, and possible reinfection of the recovered population are also considered in the model. Applying some recent techniques, we showed that the proposed system converted to a COVID-19 model with fractional order disease transmission, where order of the fractional derivative ( α ) in the force of infection function represents the memory effect in disease transmission. We studied some mathematical properties of this newly formulated model and determined the basic reproduction number (R 0 ). Furthermore, we estimated several epidemiological parameters of the newly developed fractional order model (including memory index α ) by fitting the model to the daily reported COVID-19 cases from Russia, South Africa, UK, and USA, respectively, for the time period March 01, 2020, till December 01, 2021. Variance-based Sobol's global sensitivity analysis technique is used to measure the effect of different important model parameters (including α ) on the number of COVID-19 waves in a location (W C ). Our findings suggest that α along with the average transmission rate of the undetected (symptomatic and asymptomatic) cases in the community (β 1 ) are mainly influencing multiple COVID-19 waves in those four locations. Numerically, we identified the regions in the parameter space of α andβ 1 for which multiple COVID-19 waves are occurring in those four locations. Furthermore, our findings suggested that increasing memory effect in disease transmission ( α → 0) may decrease the possibility of multiple COVID-19 waves and as well as reduce the severity of disease transmission in those four locations. Based on all the results, we try to identify a few non-pharmaceutical control strategies that may reduce the risk of further SARS-CoV-2 waves in Russia, South Africa, UK, and USA, respectively.

Dual-domain analysis of gun violence incidents in the United States

This paper applies new and recently introduced approaches to study trends in gun violence in the United States. We use techniques in both the time and frequency domain to provide a more complete understanding of gun violence dynamics. We analyze gun violence incidents on a state-by-state basis as recorded by the Gun Violence Archive. We have numerous specific phenomena of focus, including periodicity of incidents, locations in time where behavioral changes occur, and shifts in gun violence patterns since April 2020. First, we implement a recently introduced method of spectral density estimation for nonstationary time series to investigate periodicity on a state-by-state basis, including revealing where periodic behaviors change with time. We can also classify different patterns of behavioral changes among the states. We then aim to understand the most significant shifts in gun violence since numerous key events in 2020, including the COVID-19 pandemic, lockdowns, and periods of civil unrest. Our dual-domain analysis provides a more thorough understanding and challenges numerous widely held conceptions regarding the prevalence of gun violence incidents.

Temporal and spatial evolution of the distribution related to the number of COVID-19 pandemic

This work systematically conducts a data analysis based on the numbers of both cumulative and daily confirmed COVID-19 cases and deaths in a time span through April 2020 to June 2022 for over 200 countries around the world. Such research feature aims to reveal the temporal and spatial evolution of the country-level distribution observed in COVID-19 pandemic, and obtains some interesting results as follows. (1) The distributions of the numbers for cumulative confirmed cases and deaths obey power-law in early stages of COVID-19 and stretched exponential function in subsequent course. (2) The distributions of the numbers for daily confirmed cases and deaths obey power-law in early and late stages of COVID-19 and stretched exponential function in middle stages. The crossover region between power-law and stretched exponential behavior seems to depend on the evolution of "infection" event and "death" event. Such observation implies a kind of important symmetry related to the dynamics process of COVID-19 spreading. (3) The distributions of the normalized numbers for each metric show a temporal scaling behavior in 2-year period, and are well described by stretched exponential function. The observation of power-law and stretched exponential behavior in such country-level distributions suggests underlying intrinsic dynamics of a virus spreading process in human interconnected society. And thus it is important for understanding and mathematically modeling the COVID-19 pandemic.

The CP-ABM approach for modelling COVID-19 infection dynamics and quantifying the effects of non-pharmaceutical interventions

The motivation for this research is to develop an approach that reliably captures the disease dynamics of COVID-19 for an entire population in order to identify the key events driving change in the epidemic through accurate estimation of daily COVID-19 cases. This has been achieved through the new CP-ABM approach which uniquely incorporates Change Point detection into an Agent Based Model taking advantage of genetic algorithms for calibration and an efficient infection centric procedure for computational efficiency. The CP-ABM is applied to the Northern Ireland population where it successfully captures patterns in COVID-19 infection dynamics over both waves of the pandemic and quantifies the significant effects of non-pharmaceutical interventions (NPI) on a national level for lockdowns and mask wearing. To our knowledge, there is no other approach to date that has captured NPI effectiveness and infection spreading dynamics for both waves of the COVID-19 pandemic for an entire country population.

An active learning-based approach for screening scholarly articles about the origins of SARS-CoV-2

To build a full picture of previous studies on the origins of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), this paper exploits an active learning-based approach to screen scholarly articles about the origins of SARS-CoV-2 from many scientific publications. In more detail, six seed articles were utilized to manually curate 170 relevant articles and 300 nonrelevant articles. Then, an active learning-based approach with three query strategies and three base classifiers is trained to screen the articles about the origins of SARS-CoV-2. Extensive experimental results show that our active learning-based approach outperforms traditional counterparts, and the uncertain sampling query strategy performs best among the three strategies. By manually checking the top 1,000 articles of each base classifier, we ultimately screened 715 unique scholarly articles to create a publicly available peer-reviewed literature corpus, COVID-Origin. This indicates that our approach for screening articles about the origins of SARS-CoV-2 is feasible.

Topological Properties, Spectra Analysis, and Consensus Problems for a Class of Network Models Based on m-Fission Operation

The network model, especially the network model constructed by network operation, is an important tool to study complex networks. Many topological and dynamic properties of complex networks can be studied in this way. In this article, the m -fission operation is constructed based on the phenomenon of node splitting in the network, which is quite common in complex networks. Many network models, including dual Sierpinski gaskets, are built based on this operation, but it has never been systematically studied. Then, the topological and dynamic properties of the m -fission operation and the corresponding iterative fission network model are studied, and the influence of the operation on the network structure is revealed. Among them, the topological properties of the network include diameter, degree distribution, clustering coefficient, average distance, and modularity. By studying these properties, it can be concluded that the iterative fission network is a fractal homogeneous network with high clustering and high community characteristics. Since the dynamic properties are closely related to the spectrum of the Laplacian matrix corresponding to the network, the iterative relation of the spectrum in operation is studied, and the complete solution of the spectrum of the iterative fission network is obtained. Based on the above results, we calculate the analytical expressions of the characteristic quantities related to the dynamic properties on the network, including the Kirchhoff index and the average of hitting times. Finally, due to the close connection between the network model and the system, we further analyzed the consensus problems on the system corresponding to the network, including convergence rate, delay robustness, first-order noise coherence, and second-order noise coherence.

MODELING THE DYNAMICS OF COVID-19 TRANSMISSION IN INDIA: SOCIAL DISTANCING, REGIONAL SPREAD AND HEALTHCARE CAPACITY

In the new paradigm of health-centric governance, policymakers are in constant need of appropriate metrics to determine suitable policies in a non-arbitrary fashion. To this end, in this paper, a compartmentalized model for the transmission of COVID-19 is developed, with a socially distanced compartment added to the model. The modification allows for administrators to quantify the extent to which voluntary social distancing norms are followed, and address restrictions accordingly. Modifications are also made to incorporate inter-region migration, and suitable metrics are proposed to quantify the impact of migration on the rise of cases. The healthcare capacity is modeled and a method is developed to study the consequences of the saturation of the healthcare system. The model and related measures are used to study the nature of the transmission and spread of COVID-19 in India, and appropriate insights are drawn.

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

Power law in COVID-19 cases in China

The novel coronavirus (COVID-19) was first identified in China in December 2019. Within a short period of time, the infectious disease has spread far and wide. This study focuses on the distribution of COVID-19 confirmed cases in China-the original epicentre of the outbreak. We show that the upper tail of COVID-19 cases in Chinese cities is well described by a power law distribution, with exponent around one in the early phases of the outbreak (when the number of cases was growing rapidly) and less than one thereafter. This finding is significant because it implies that (i) COVID-19 cases in China is heavy tailed and disperse; (ii) a few cities account for a disproportionate share of COVID-19 cases; and (iii) the distribution generally has no finite mean or variance. We find that a proportionate random growth model predicated by Gibrat's law offers a plausible explanation for the emergence of a power law in the distribution of COVID-19 cases in Chinese cities in the early phases of the outbreak.

Inventions of Interventions: Data Driven Strategies in Pandemic Research and Control

Faced with a rapidly evolving virus, inventors must seek to experiment, iterate and deploy both creative and effective solutions. Supported by empirical model-driven analysis, this paper delves into fundamental paradoxes and biases in the context of epidemic research, increasing awareness at every stage of the clinical trial; ranging from hypothesizing to sampling, and analyses to fake data detection. Critically, the paper also presents novel ideas that demonstrate how the paradoxes and biases covered play into technology development and deployment to combat the surging pandemic, COVID-19.

The allometric propagation of COVID-19 is explained by human travel

We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, and even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles traveled in the US. Together, air and vehicular travel explained 70% of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

In search of peak human athletic potential: A mathematical investigation

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect," where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatiotemporal trends in group composition.

Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.

Functional observability and target state estimation in large-scale networks

Observing the states of a network is fundamental to our ability to explore and control the dynamics of complex natural, social, and technological systems. The problem of determining whether the system is observable has been addressed by network control researchers over the past decade. Progress on the further problem of actually designing and implementing efficient algorithms to infer the states from limited measurements has been hampered by the high dimensionality of large-scale networks. Noting that often only a small number of state variables in a network are essential for control, intervention, and monitoring purposes, this work develops a graph-based theory and highly scalable methods that achieve accurate estimation of target variables of network systems with minimal sensing and computational resources.

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to 1) determine the minimal set of required sensors and 2) design the corresponding state observer of minimum order. Compared with the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and fewer computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyberattacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

The power-law distribution in the geometrically growing system: Statistic of the COVID-19 pandemic

The power-law distribution is ubiquitous and seems to have various mechanisms. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log-completely squared chi distribution with one degree of freedom (log-CS χ₁), which reaches asymptotically a power-law distribution, or by a lognormal distribution, which has an infinite asymptotic slope, at the upper limit. For the log-CS χ₁, the asymptotic exponent of the power-law or the slope in a log-log diagram seems to be related only to the variances of the system parameters and their mutual correlation but independent of an initial distribution of the system or any mean value of parameters. We can take the log-CS χ₁ as a unique approximation when the system should have a singular initial distribution. The mechanism shows comprehensiveness to be applicable to wide practice. We derive a simple formula for Zipf's exponent, which will probably demand that the exponent should be near -1 rather than exactly -1. We show that this approach can explain statistics of the COVID-19 pandemic.

Trends in COVID-19 prevalence and mortality: A year in review

This paper introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of virulence matrices to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce three-way inconsistency analysis to determine anomalous countries with respect to three attributes: countries' COVID-19 cases, deaths and human development indices. We demonstrate the most anomalous countries across these three measures are Pakistan, the United States and the United Arab Emirates.

Basic Study on Scale-Free Networks and Targeted Antivirus Prophylaxis Supported by Information Communication Tools

With the aim of slowing the spread of infectious disease in the earliest phase of an outbreak, we performed visual simulations using scale-free networks focused on circumstances such as “normal” daily life, pandemic outbreaks, and the Fukushima nuclear accident following the Great East Japan Earthquake of 2011. Due to limitations associated with face-to-face contacts and delays in the timing of intake of iodine tablets, iodine preparations for protecting the thyroid gland could be taken effectively by only 5% of the population in the aftermath of the Fukushima nuclear accident. For targeted antivirus prophylaxis (TAP) to be more effective, timing of the distribution of anti-viral medication needs to be planned well in advance and instructions to “take it now!” must be communicated effectively in a timely manner. The results of this study suggest that information communication technology (e.g., pulse oximeters, mobile phones) can play an important role in managing TAP policies.

Do population density, socio-economic ranking and Gini Index of cities influence infection rates from coronavirus? Israel as a case study

A prominent characteristic of the COVID-19 pandemic is the marked geographic variation in COVID-19 prevalence. The objective of the current study is to assess the influence of population density and socio-economic measures (socio-economic ranking and the Gini Index) across cities on coronavirus infection rates. Israel provides an interesting case study based on the highly non-uniform distribution of urban populations, the existence of one of the most densely populated cities in the world and diversified populations. Moreover, COVID19 challenges the consensus regarding compact planning design. Consequently, it is important to analyze the relationship between COVID19 spread and population density. The outcomes of our study show that ceteris paribus projected probabilities to be infected from coronavirus rise with population density from 1.6 to 2.72% up to a maximum of 5.17-5.238% for a population density of 20,282-20,542 persons per square kilometer (sq. km.). Above this benchmark, the anticipated infection rate drops up to 4.06-4.50%. Projected infection rates of 4.06-4.50% are equal in cities, towns and regional councils (Local Authorities) with the maximal population density of 26,510 and 11,979-13,343 persons per sq. km. A possible interpretation is that while denser cities facilitate human interactions, they also enable and promote improved health infrastructure. This, in turn, contributes to medical literacy, namely, elevated awareness to the benefits associated with compliance with hygienic practices (washing hands), social distancing rules and wearing masks. Findings may support compact planning design principles, namely, development of dense, mixed use, walkable and transit accessible community design in compact and polycentric regions. Indeed, city planners should weigh the costs and benefits of many risk factors, including the COVID19 pandemic.

Spatial scales, patterns, and positivity trends of SARS-CoV-2 pandemics in mass rapid antigen testing in Slovakia

We study geographical epidemic scales and patterns and positivity trends of SARS-CoV-2 pandemics in mass antigen testing in Slovakia in 2020. The observed test positivity was exponentially distributed with a long scale exponential spatial trend, and its characteristic correlation length was approximately 10 km. Spatial scales also play an important role in test positivity reduction between two consecutive testing rounds. While test positivity decreased in all counties, it increased in individual municipalities with low test positivity in the earlier testing round in a way statistically different from a mean-reversion process. Also, non-residents testing influences the mass testing results as test positivity of non-residents was higher than of residents when testing was offered only in municipalities with the highest positivity in previous rounds. Our results provide direct guidance for pandemic geographical data surveillance and epidemic response management.

Efficiency of communities and financial markets during the 2020 pandemic

This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided.

Epidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases

While the mathematical laws of uncontrolled epidemic spreading are well known, the statistical physics of coronavirus epidemics with containment measures is currently lacking. The modelling of available data of the first wave of the Covid-19 pandemic in 2020 over 230 days, in different countries representative of different containment policies is relevant to quantify the efficiency of these policies to face the containment of any successive wave. At this aim we have built a 3D phase diagram tracking the simultaneous evolution and the interplay of the doubling time,T_d, and the reproductive number,R_tmeasured using the methodological definition used by the Robert Koch Institute. In this expanded parameter space three different main phases,supercritical,criticalandsubcriticalare identified. Moreover, we have found that in thesupercriticalregime withR_t> 1 the doubling time is smaller than 40 days. In this phase we have established the power law relation betweenT_dand (R_t- 1)^-νwith the exponentνdepending on the definition of reproductive number. In thesubcriticalregime whereR_t< 1 andT_d> 100 days, we have identified arrested metastable phases whereT_dis nearly constant.

Metastable states in plateaus and multi-wave epidemic dynamics of Covid-19 spreading in Italy

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 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 Covid-19 dynamics in Italy and its administrative Regions. The supercritical regime is mathematically characterized by (i) the power law of Td vs. [Rt(t) - 1] and (ii) the exponential behaviour of Td vs. time, either in the first and in the second wave. The novel 3D phase diagram shows clearly metastable states appearing before and after the second wave critical regime. for loosening quarantine and tracing of actives cases. The metastable states are precursors of the abrupt onset of a next nascent wave supercritical regime. This dynamic description allows epidemics predictions needed by policymakers interested to point to the target "zero infections" with the elimination of SARS-CoV-2, using the Finding mobile Tracing policy joint with vaccination-campaign, in order to avoid the emergence of recurrent new variants of SARS-CoV-2 virus, accompined by recurrent long lockdowns, with large economical losses, and large number of fatalities.

Nonuniversal power-law dynamics of susceptible infected recovered models on hierarchical modular networks

Power-law (PL) time-dependent infection growth has been reported in many COVID-19 statistics. In simple susceptible infected recovered (SIR) models, the number of infections grows at the outbreak as I(t)∝t^{d-1} on d-dimensional Euclidean lattices in the endemic phase, or it follows a slower universal PL at the critical point, until finite sizes cause immunity and a crossover to an exponential decay. Heterogeneity may alter the dynamics of spreading models, and spatially inhomogeneous infection rates can cause slower decays, posing a threat of a long recovery from a pandemic. COVID-19 statistics have also provided epidemic size distributions with PL tails in several countries. Here I investigate SIR-like models on hierarchical modular networks, embedded in 2d lattices with the addition of long-range links. I show that if the topological dimension of the network is finite, average degree-dependent PL growth of prevalence emerges. Supercritically, the same exponents as those of regular graphs occur, but the topological disorder alters the critical behavior. This is also true for the epidemic size distributions. Mobility of individuals does not affect the form of the scaling behavior, except for the d=2 lattice, but it increases the magnitude of the epidemic. The addition of a superspreader hot spot also does not change the growth exponent and the exponential decay in the herd immunity regime.

Power-law growth of the COVID-19 fatality incidents in Europe

We report on the dynamic scaling of the diffusion growth phase of the COVID-19 epidemic in Europe. During this initial diffusion stage, the European countries implemented unprecedented mitigation polices to delay and suppress the disease contagion, although not in a uniform way or timing. Despite this diversity, we find that the reported fatality cases grow following a power law in all European countries we studied. The difference among countries is the value of the power-law exponent 3.5 < α < 8.0. This common attribute can prove a practical diagnostic tool, allowing reasonable predictions for the growth rate from very early data at a country level. We propose a model for the disease-causing interactions, based on a mechanism of human decisions and risk taking in interpersonal associations. The model describes the observed statistical distribution and contributes to the discussion on basic assumptions for homogeneous mixing or for a network perspective in epidemiological studies of COVID-19.

Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19

This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories and extremes, and show greater persistence in anomalies over time.

The allometric propagation of COVID-19 is explained by human travel

We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, and even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles travelled in the US. Together, air and vehicular travel explained 70 % of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Nonparametric Methods

Containment strategies to combat epidemics such as SARS-CoV-2/COVID-19 require the availability of epidemiological parameters, e.g., the effective reproduction number. Parametric models such as the commonly used susceptible-infected-removed (SIR) compartment models fitted to observed incidence time series have limitations due to the time-dependency of the parameters. Furthermore, fatalities are delayed with respect to the counts of new cases, and the reproduction cycle leads to periodic patterns in incidence time series. Therefore, based on comprehensible nonparametric methods including time-delay correlation analyses, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented using publicly available time-series data on prevalence and fatalities. The estimates for Germany are compared with the results for seven other countries (France, Italy, the United States of America, the United Kingdom, Spain, Switzerland, and Brazil). The duration from diagnosis to death resulting from delay-time correlations turns out to be 13 days with high accuracy for Germany and Switzerland. For the other countries, the time-to-death durations have wider confidence intervals. With respect to the German data, the two time series of new cases and fatalities exhibit a strong coherence. Based on the time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated. The temporal median of the instantaneous fatality-case ratio with time lag of 13 days between cases and deaths for Germany turns out to be 0.02. Time courses of asymptotic fatality-case ratios are presented for other countries, which substantially differ during the first half of the pandemic but converge to a narrow range with standard deviation 0.0057 and mean 0.024. Similar results are obtained from comparing time courses of instantaneous fatality-case ratios with optimal delay for the 8 exemplarily chosen countries. The basic reproduction number, R0, for Germany is estimated to be between 2.4 and 3.4 depending on the generation time, which is estimated based on a delay autocorrelation analysis. Resonances at about 4 days and 7 days are observed, partially attributable to weekly periodicity of sampling. The instantaneous (time-dependent) reproduction number is estimated from the incident (counts of new) cases, thus allowing us to infer the temporal behaviour of the reproduction number during the epidemic course. The time course of the reproduction number turns out to be consistent with the time-dependent per capita growth.

COVID-19 second wave mortality in Europe and the United States

This paper introduces new methods to analyze the changing progression of COVID-19 cases to deaths in different waves of the pandemic. First, an algorithmic approach partitions each country or state's COVID-19 time series into a first wave and subsequent period. Next, offsets between case and death time series are learned for each country via a normalized inner product. Combining these with additional calculations, we can determine which countries have most substantially reduced the mortality rate of COVID-19. Finally, our paper identifies similarities in the trajectories of cases and deaths for European countries and U.S. states. Our analysis refines the popular conception that the mortality rate has greatly decreased throughout Europe during its second wave of COVID-19; instead, we demonstrate substantial heterogeneity throughout Europe and the U.S. The Netherlands exhibited the largest reduction of mortality, a factor of 16, followed by Denmark, France, Belgium, and other Western European countries, greater than both Eastern European countries and U.S. states. Some structural similarity is observed between Europe and the United States, in which Northeastern states have been the most successful in the country. Such analysis may help European countries learn from each other's experiences and differing successes to develop the best policies to combat COVID-19 as a collective unit.

Association between COVID-19 cases and international equity indices

This paper analyzes the impact of COVID-19 on the populations and equity markets of 92 countries. We compare country-by-country equity market dynamics to cumulative COVID-19 case and death counts and new case trajectories. First, we examine the multivariate time series of cumulative cases and deaths, particularly regarding their changing structure over time. We reveal similarities between the case and death time series, and key dates that the structure of the time series changed. Next, we classify new case time series, demonstrate five characteristic classes of trajectories, and quantify discrepancy between them with respect to the behavior of waves of the disease. Finally, we show there is no relationship between countries' equity market performance and their success in managing COVID-19. Each country's equity index has been unresponsive to the domestic or global state of the pandemic. Instead, these indices have been highly uniform, with most movement in March.

Universal Epidemic Curve for COVID-19 and Its Usage for Forecasting

We construct a universal epidemic curve for COVID-19 using the epidemic curves of eight nations that have reached saturation for the first phase and then fit an eight-degree polynomial that passes through the universal curve. We take India's epidemic curve up to January 1, 2021 and match it with the universal curve by minimizing square-root error between the model prediction and actual value. The constructed curve has been used to forecast epidemic evolution up to February 25, 2021. The predictions of our model and those of supermodel for India (Agrawal et al. in Indian J Med Res, 2020; Vidyasagar et al. in https://www.iith.ac.in/~m_vidyasagar/arXiv/Super-Model.pdf, 2020) are reasonably close to each other considering the uncertainties in data fitting.

Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic

We apply a versatile growth model, whose growth rate is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and North America. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to policymakers and health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the final death toll but also the risk of a resurgence of infections.

The impact of human mobility networks on the global spread of COVID-19

Human mobility networks are crucial for a better understanding and controlling the spread of epidemics. Here, we study the impact of human mobility networks on the COVID-19 onset in 203 different countries. We use exponential random graph models to perform an analysis of the country-to-country global spread of COVID-19. We find that most countries had similar levels of virus spreading, with only a few acting as the main global transmitters. Our evidence suggests that migration and tourism inflows increase the probability of COVID-19 case importations while controlling for contiguity, continent co-location and sharing a language. Moreover, we find that air flights were the dominant mode of transportation while male and returning travellers were the main carriers. In conclusion, a mix of mobility and geography factors predicts the COVID-19 global transmission from one country to another. These findings have implications for non-pharmaceutical public health interventions and the management of transborder human circulation.

Drawing transmission graphs for COVID-19 in the perspective of network science

When we consider a probability distribution about how many COVID-19-infected people will transmit the disease, two points become important. First, there could be super-spreaders in these distributions/networks and second, the Pareto principle could be valid in these distributions/networks regarding estimation that 20% of cases were responsible for 80% of local transmission. When we accept that these two points are valid, the distribution of transmission becomes a discrete Pareto distribution, which is a kind of power law. Having such a transmission distribution, then we can simulate COVID-19 networks and find super-spreaders using the centricity measurements in these networks. In this research, in the first we transformed a transmission distribution of statistics and epidemiology into a transmission network of network science and second we try to determine who the super-spreaders are by using this network and eigenvalue centrality measure. We underline that determination of transmission probability distribution is a very important point in the analysis of the epidemic and determining the precautions to be taken.

Epidemic plateau in critical susceptible-infected-removed dynamics with nontrivial initial conditions

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical susceptible-infected-removed (SIR) dynamics. In traditional analyses of the critical SIR model, the critical dynamical regime is started from a single infected node. The application of containment measures to an ongoing epidemic, however, has the effect to make the system enter in its critical regime with a number of infected individuals potentially large. We describe how such nontrivial starting conditions affect the critical behavior of the SIR model. We perform a theoretical and large-scale numerical investigation of the model. We show that the expected outbreak size is an increasing function of the initial number of infected individuals, while the expected duration of the outbreak is a nonmonotonic function of the initial number of infected individuals. Also, we precisely characterize the magnitude of the fluctuations associated with the size and duration of the outbreak in critical SIR dynamics with nontrivial initial conditions. Far from herd immunity, fluctuations are much larger than average values, thus indicating that predictions of plateauing time series may be particularly challenging.

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and the United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth, a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

On the temporal spreading of the SARS-CoV-2

The behaviour of SARS-CoV-2 virus is certainly one of the most challenging in contemporary world. Although the mathematical modelling of the virus has made relevant contributions, the unpredictable behaviour of the virus is still not fully understood. To identify some aspects of the virus elusive behaviour, we focused on the temporal characteristics of its course. We have analysed the latency trends the virus has realized worldwide, the outbreak of the hot spots, and the decreasing trends of the pandemic. We found that the spatio-temporal pandemic dynamics shows a complex behaviour. As with physical systems, these changes in the pandemic's course, which we have called transitional stages of contagion, highlight shared characteristics in many countries. The main results of this work is that the pandemic progression rhythms have been clearly identified for each country, providing the processes and the stages at which the virus develops, thus giving important information on the activation of containment and control measures.

Calculation of epidemic arrival time distributions using branching processes

The rise of the World Airline Network over the past century has led to sharp changes in our notions of "distance" and "closeness"-in terms of both trade and travel, but also (less desirably) with respect to the spread of disease. When novel pathogens are discovered, countries, cities, and hospitals are caught trying to predict how much time they have to prepare. In this paper, by considering the early stages of epidemic spread as a simple branching process, we derive the full probability distribution of arrival times. We are able to rederive a number of past arrival time results (in suitable limits) and demonstrate the robustness of our approach, both to parameter values far outside the traditionally considered regime and to errors in the parameter values used. The branching process approach provides some theoretical justification to the "effective distance" introduced by Brockmann and Helbing [Science 342, 1337 (2013)SCIEAS0036-807510.1126/science.1245200]; however, we also observe that when compared to real-world data, the predictive power of all methods in this class is significantly lower than has been previously reported.

COVID-19 Pandemic: Power Law Spread and Flattening of the Curve

In this paper, we analyze the real-time infection data of COVID-19 epidemic for nine nations. Our analysis is up to May 04, 2020. South Korea, China, Italy, France, Spain, and Germany have either flattened or close to flattening their epidemic curves. USA and Japan have transitioned to a linear regime, while India is still in a power-law phase. We argue that the transition from an exponential regime to a succession of power-law regimes is a good indicator for flattening of the epidemic curve. We also argue that lockdowns, long-term community transmission, and the transmission by asymptomatic carriers traveling long distances may be inducing the power-law growth of the epidemic.