An analysis of COVID-19 spread based on fractal interpolation and fractal dimension

Key risk factors associated with fractal dimension based geographical clustering of COVID-19 data in the Flemish and Brussels region, Belgium

Introduction

COVID-19 remains a major concern globally. Therefore, it is important to evaluate COVID-19's rapidly changing trends. The fractal dimension has been proposed as a viable method to characterize COVID-19 curves since epidemic data is often subject to considerable heterogeneity. In this study, we aim to investigate the association between various socio-demographic factors and the complexity of the COVID-19 curve as quantified through its fractal dimension.

Methods

We collected population indicators data (ethnic composition, socioeconomic status, number of inhabitants, population density, the older adult population proportion, vaccination rate, satisfaction, and trust in the government) at the level of the statistical sector in Belgium. We compared these data with fractal dimension indicators of COVID-19 incidence between 1 January - 31 December 2021 using canonical correlation analysis.

Results

Our results showed that these population indicators have a significant association with COVID-19 incidences, with the highest explanatory and predictive power coming from the number of inhabitants, population density, and ethnic composition.

Conclusion

It is important to monitor these population indicators during a pandemic, especially when dealing with targeted interventions for a specific population.

Fractal dimension analysis of stock prices of selected resulting companies after mergers and acquisitions

This study focuses on the short-run wealth of listed firms' shareholders. Currently, all of the resulting organizations offer competitive pricing tactics to create a superior environment for our ongoing establishment. Some time ago, it was noted that a merger occurred, although some functions and technology integration remained with the previous structure. In this paper, it has been discovered that merger and acquisition deals have an impact on the firm's value; in other words, we can view it as shareholders' wealth or unit depending on the stock price after the announcement of merger and acquisition deals in the short term. Furthermore, we focused on influencing variables on stock prices after the announcement of merger and acquisition transactions, which is measured as a percentage change in the stock prices of the listed resulting firms. Furthermore, this research is based on secondary data sources from reputable organizations. It primarily uses the NSE database and website to evaluate announcements and stock prices of the twenty-nine publicly traded companies. Markets respond to investors' emotions and market expertise. When acquirers have a strong market position, market capitalization rises in other segments. However, it is declining due to a lack of supportive finances. To determine the impact of merger and acquisition announcement deals on stock price changes, average abnormal return and cumulative average abnormal return with the capital asset pricing model (CAPM) (CAPM reaction to changes) were used to identify the acquiring company's stock price reaction. We investigated its impact on the fluctuation of share prices posted on stock exchanges using fractal interpolation functions. This is due to greater investment by acquirer businesses in target companies as well as investor expectations for specific stock market strongholds.

Fractal dimension based geographical clustering of COVID-19 time series data

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

Dimensional study of COVID-19 via fractal functions

The present paper deals with the modeling of the COVID-19 via fractal interpolation function (FIF) and the estimation of the dimension of constructed FIF. Further, we determine the adjoint of the fractal operator defined onL 2 space associated with the FIF.

A fractal-fractional COVID-19 model with a negative impact of quarantine on the diabetic patients

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

TL-med: A Two-stage transfer learning recognition model for medical images of COVID-19

The recognition of medical images with deep learning techniques can assist physicians in clinical diagnosis, but the effectiveness of recognition models relies on massive amounts of labeled data. With the rampant development of the novel coronavirus (COVID-19) worldwide, rapid COVID-19 diagnosis has become an effective measure to combat the outbreak. However, labeled COVID-19 data are scarce. Therefore, we propose a two-stage transfer learning recognition model for medical images of COVID-19 (TL-Med) based on the concept of "generic domain-target-related domain-target domain". First, we use the Vision Transformer (ViT) pretraining model to obtain generic features from massive heterogeneous data and then learn medical features from large-scale homogeneous data. Two-stage transfer learning uses the learned primary features and the underlying information for COVID-19 image recognition to solve the problem by which data insufficiency leads to the inability of the model to learn underlying target dataset information. The experimental results obtained on a COVID-19 dataset using the TL-Med model produce a recognition accuracy of 93.24%, which shows that the proposed method is more effective in detecting COVID-19 images than other approaches and may greatly alleviate the problem of data scarcity in this field.

On fractal-fractional Covid-19 mathematical model

In this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.

Omicron: a mysterious variant of concern

Omicron (B.1.1.529), a highly mutated SARS-CoV-2 variant, has emerged in the south of African continent in the November 2021. The spike protein of Omicron has 26 amino acid mutations, which makes it distinct from the other variants of concern. Researches are underway to know the virulence and transmission rate of Omicron variant. In this letter, the seven-day moving average of most affected Omicron variant countries Denmark, Germany, India, Netherlands, South Africa and UK has been investigated and compared with each other. Further, the seven-day average of daily positive Omicron cases of the prescribed countries has been predicted for the months of December 2021, January 2022 and February 2022 using the fractal interpolation method. Results elucidate that the curve of daily positive case follows the same pattern even though the new variant of concern, Omicron added in the existing variants.

Simulations of Lévy Walk

The simulation of stable distributions was performed to study an ideal movement pattern for the spread of a virus using an autonomous carrier. It has been observed that Lévy walks are the most ideal way to spread and further study was done on how the parameters in Lévy distribution affect the spread.

WOANet: Whale optimized deep neural network for the classification of COVID-19 from radiography images

Coronavirus Diseases (COVID-19) is a new disease that will be declared a global pandemic in 2020. It is characterized by a constellation of traits like fever, dry cough, dyspnea, fatigue, chest pain, etc. Clinical findings have shown that the human chest Computed Tomography(CT) images can diagnose lung infection in most COVID-19 patients. Visual changes in CT scan due to COVID-19 is subjective and evaluated by radiologists for diagnosis purpose. Deep Learning (DL) can provide an automatic diagnosis tool to relieve radiologists' burden for quantitative analysis of CT scan images in patients. However, DL techniques face different training problems like mode collapse and instability. Deciding on training hyper-parameters to adjust the weight and biases of DL by a given CT image dataset is crucial for achieving the best accuracy. This paper combines the backpropagation algorithm and Whale Optimization Algorithm (WOA) to optimize such DL networks. Experimental results for the diagnosis of COVID-19 patients from a comprehensive COVID-CT scan dataset show the best performance compared to other recent methods. The proposed network architecture results were validated with the existing pre-trained network to prove the efficiency of the network.

Optimization strategies of human mobility during the COVID-19 pandemic: A review

The impact of the ongoing COVID-19 pandemic is being felt in all spheres of our lives - cutting across the boundaries of nation, wealth, religions or race. From the time of the first detection of infection among the public, the virus spread though almost all the countries in the world in a short period of time. With humans as the carrier of the virus, the spreading process necessarily depends on the their mobility after being infected. Not only in the primary spreading process, but also in the subsequent spreading of the mutant variants, human mobility plays a central role in the dynamics. Therefore, on one hand travel restrictions of varying degree were imposed and are still being imposed, by various countries both nationally and internationally. On the other hand, these restrictions have severe fall outs in businesses and livelihood in general. Therefore, it is an optimization process, exercised on a global scale, with multiple changing variables. Here we review the techniques and their effects on optimization or proposed optimizations of human mobility in different scales, carried out by data driven, machine learning and model approaches.

Agent-based analysis of contagion events according to sourcing locations

The first human infected with the Covid-19 virus was traced to a seafood market in Wuhan, China. Research shows that there are comparable types of viruses found in different and mutually distant areas. This raises several questions: what if the virus originated in another location? How will future waves of epidemics behave if they originate from different locations with a smaller/larger population than Wuhan? To explore these questions, we implement an agent-based model within fractal cities. Cities radiate gravitational social attraction based on their Zipfian population. The probability and predictability of contagion events are analyzed by examining fractal dimensions and lacunarity. Results show that weak gravitational forces of small locations help dissipate infections across country quicker if the pathogen had originated from that location. Gravitational forces of large cities help contain infections within them if they are the starting locations for the pathogen. Greater connectedness and symmetry allow for a more predictable epidemic outcome since there are no obstructions to spreading. To test our hypothesis, we implement datasets from two countries, Sierra Leone and Liberia, and two diseases, Ebola and Covid-19, and obtain the same results.

The second and third waves in India: when will the pandemic be culminated?

An unprecedented upsurge of COVID-19-positive cases and deaths is currently being witnessed across India. According to WHO, India reported an average of 3.9 lakhs of new cases during the first week of May 2021 which equals 47% of new cases reported globally and 276 daily cases per million population. In this letter, the concept of SIR and fractal interpolation models is applied to predict the number of positive cases in India by approximating the epidemic curve, where the epidemic curve denotes the two-dimensional graphical representation of COVID-19-positive cases in which the abscissa denotes the time, while the ordinate provides the number of positive cases. In order to estimate the epidemic curve, the fractal interpolation method is implemented on the prescribed data set. In particular, the vertical scaling factors of the fractal function are selected from the SIR model. The proposed fractal and SIR model can also be explored for the assessment and modeling of other epidemics to predict the transmission rate. This letter investigates the duration of the second and third waves in India, since the positive cases and death cases of COVID-19 in India have been highly increasing for the past few weeks, and India is in a midst of a catastrophizing second wave. The nation is recording more than 120 million cases of COVID-19, but pandemics are still concentrated in most states. In order to predict the forthcoming trend of the outbreaks, this study implements the SIR and fractal models on daily positive cases of COVID-19 in India and its provinces, namely Delhi, Karnataka, Tamil Nadu, Kerala and Maharashtra.

An exploration of fractal-based prognostic model and comparative analysis for second wave of COVID-19 diffusion

The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the data set of the number of deaths per day and the number of infected cases per day of the most affected countries, the USA, Brazil, Russia, India, and the UK, have been considered in the first and second waves. The correlation fractal dimension has been estimated for the prescribed data sets of COVID-19, and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance, has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to visualize the transmission rate in the both times.

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.

The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally

In December 2019, China announced the breakout of a new virus identified as coronavirus SARS-CoV-2 (COVID-19), which soon grew exponentially and resulted in a global pandemic. Despite strict actions to mitigate the spread of the virus in various countries, COVID-19 resulted in a significant loss of human life in 2020 and early 2021. To better understand the dynamics of the spread of COVID-19, evidence of its chaotic behavior in the US and globally was evaluated. A 0-1 test was used to analyze the time-series data of confirmed daily COVID-19 cases from 1/22/2020 to 12/13/2020. The results show that the behavior of the COVID-19 pandemic was chaotic in 55% of the investigated countries. Although the time-series data for the entire US was not chaotic, 39% of individual states displayed chaotic infection spread behavior based on the reported daily cases. Overall, there is evidence of chaotic behavior of the spread of COVID-19 infection worldwide, which adds to the difficulty in controlling and preventing the current pandemic.

On the use of growth models to understand epidemic outbreaks with application to COVID-19 data

The initial phase dynamics of an epidemic without containment measures is commonly well modelled using exponential growth models. However, in the presence of containment measures, the exponential model becomes less appropriate. Under the implementation of an isolation measure for detected infectives, we propose to model epidemic dynamics by fitting a flexible growth model curve to reported positive cases, and to infer the overall epidemic dynamics by introducing information on the detection/testing effort and recovery and death rates. The resulting modelling approach is close to the Susceptible-Infectious-Quarantined-Recovered model framework. We focused on predicting the peaks (time and size) in positive cases, active cases and new infections. We applied the approach to data from the COVID-19 outbreak in Italy. Fits on limited data before the observed peaks illustrate the ability of the flexible growth model to approach the estimates from the whole data.