Framework of fractals in data analysis: theory and interpretation.

This special issue is a compilation of pioneering research articles that explore the robustness of fractal theories to address and analyse the complexity of real-time data under the topic "Framework of Fractals in Data Analysis: Theory and Interpretation".

Greenhouse gas emissions: A rapid submerge of the world.

The investigation of worldwide climate change is a noticeable exploration topic in the field of sciences. Outflow of greenhouse gases in the environment is the main reason behind the worldwide environmental change. Greenhouse gases retain heat from the sun and prompt the earth to become more sultry, resulting in global warming. In this article, a model based technique is proposed to forecast the future climate dynamics globally. Using past data on annual greenhouse gas emissions and per capita greenhouse gas emissions, the fractal curves are generated and a forecast model called the autoregressive integrated moving average model has been employed to anticipate the future scenario in relation to climate change and its impact on sea-level rise. It is necessary to forecast the climate conditions before the situations become acute. Policy measures aimed at lowering CO and other greenhouse gas emissions, or at least slowing down their development, will have a substantial effect on future warming of the earth.

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.

Frontiers of fractals for complex systems: recent advances and future challenges.

This special issue of the European Physical Journal Special Topics titled "Frontiers of Fractals for Complex Systems: Recent Advances and Future Challenges"  is a collection of cutting-edge research proposing the application of fractal features to the dynamics of highly nonlinear complex systems.

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.

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.

Can India develop herd immunity against COVID-19?

World Health Organization declared the novel coronavirus disease 2019 (COVID-19) outbreak to be a public health crisis of international concern. Further, it provided advice to the global community that countries should place strong measures to detect disease early, isolate and treat cases, trace contacts and promote "social distancing" measures commensurate with the risk. This study analyses the COVID-19 infection data from the top 15 affected countries in which we observed heterogeneous growth patterns of the virus. Hence, this paper applies multifractal formalism on COVID-19 data with the notion that country-specific infection rates follow a power law growth behaviour. According to the estimated generalized fractal dimension curves, the effects of drastic containment measures on the pandemic in India indicate that a significant reduction of the infection rate as its population is concern. Also, comparison results with other countries demonstrate that India has less death rate or more immunity against COVID-19.