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Coronavirus disease knocked in Wuhan city of China in December 2019 which spread quickly across the world and infected millions of people within a short span of time. COVID-19 is a fast-spreading contagious disease which is caused by SARS-CoV-2 (severe acute respiratory syndrome-coronavirus-2). Accurate time series forecasting modeling is the need of the hour to monitor and control the universality of COVID-19 effectively, which will help to take preventive measures to break the ongoing chain of infection. India is the second highly populated country in the world and in summer the temperature rises up to 50°, nowadays in many states have more than 40° temperatures. The present study deals with the development of the autoregressive integrated moving average (ARIMA) model to predict the trend of the number of COVID-19 infected people in most affected states of India and the effect of a rise in temperature on COVID-19 cases. Cumulative data of COVID-19 confirmed cases are taken for study which consists of 77 sample points ranging from 1st March 2020 to 16th May 2020 from six states of India namely Delhi (Capital of India), Madya Pradesh, Maharashtra, Punjab, Rajasthan, and Uttar Pradesh. The developed ARIMA model is further used to make 1-month ahead out of sample predictions for COVID-19. The performance of ARIMA models is estimated by comparing measures of errors for these six states which will help in understanding future trends of COVID-19 outbreak. Temperature rise shows slightly negatively correlated with the rise in daily cases. This study is noble to analyse the variation of COVID-19 cases with respect to temperature and make aware of the state governments and take precautionary measures to flatten the growth curve of confirmed cases of COVID-19 infections in other states of India, nearby countries as well.

In recent times, black carbon (BC) has attracted the interest of the researchers due to its adverse effect on human health, climate, rainfall, and global heating causing the melting of ice in the poles due to carbon deposition on it. Coal industry is the backbone of Indian economy and India being the world’s third largest producer of coal. Various mining activities are leading to spontaneous emission of black carbon in the atmosphere, especially in the IGP (Indo-Gangetic plain) region. Long-term studies related to black carbon emission in the coal regions of India are very rare. In the present study, a long-term datum of 38 years (1980–2018) for the amount of black carbon emission among the three important coal mines of India, namely Bokaro, Jharia, and Raniganj, is studied using correlation analysis, and time-series analysis along with a few other mathematical parameters. The comparison and forecast obtained using this study will be beneficial in the upcoming years, so as to gather the interest of the government, NGOs, and researchers in this area, so that new policies and preventive measures could be taken to curtail the black carbon concentration from the coal mines.

Time series analysis has been widely used by the researchers in the field of mathematical forecasting; it has been mainly used to obtain the forecast of time series dealing with pollutants, groundwater level, and stock exchange so as to study their future behavior of such time series. The present research work deals with the black carbon concentrations in three major coal mines of India namely, Bokaro, Jharia and Raniganj. In this study, a time series data last 38 years (from 1980 to 2018) obtained from a reliable source (NASA) have been considered by statistical analysis tools like mean, median, mode, standard deviation, skewness, kurtosis, coefficient of variation and time series (ARIMA (Autoregressive Integrated Moving Average)) model at 95% confidence limits have been applied. The validation of the model is tested using R-square, stationary R-square, root mean square error (RMSE), normalized Bayesian information criterion (BIC). It is observed that the model fitted very well, based on these past observations, ARIMA model is applied to obtain the prediction of the amount of black carbon emission for next 7 years 5 months (from Jun 2018 to Oct 2025). These results will help to develop new policies and preventive measures in future by the government agencies, NGOs in these areas and take a note of the seriousness and impact of such huge concentration of black carbon emission in these areas.

Highlights • The study is about the prediction of COVID-19 cases in major countries around the globe. Its Noble study. • It will help the different countries to make the decision on this virus. • ARIMA and LSSVM are the machine learning models, which computes accurate prediction with the least error. • The model provides the 99% approximate accuracy. • This manuscript will also help to all governments for preparing isolation wards, availability of medical staff, medicines requirement, the decision on lock down, economic plans, etc., Discussions about the recently identified deadly coronavirus disease (COVID-19) which originated in Wuhan, China in December 2019 are common around the globe now. This is an infectious and even life-threatening disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has rapidly spread to other countries from its originating place infecting millions of people globally. To understand future phenomena, strong mathematical models are required with the least prediction errors. In the present study, autoregressive integrated moving average (ARIMA) and least square support vector machine (LS-SVM) models are applied to the data consisting of daily confirmed cases of SARS-CoV-2 in the most affected five countries of the world for modeling and predicting one-month confirmed cases of this disease. To validate these models, the prediction results were tested by comparing it with testing data. The results revealed better accuracy of the LS-SVM model over the ARIMA model and also suggested a rapid rise of SARS-CoV-2 confirmed cases in all the countries under study. This analysis would help governments to take necessary actions in advance associated with the preparation of isolation wards, availability of medicines and medical staff, a decision on lockdown, training of volunteers, and economic plans.

Time series display irregular patterns and self-similar microstructures usually termed as fractals over a period of time, depending on several factors like climate, season, market fluctuations, growth cycles etc. Various methods are developed in mathematical modeling to investigate such trends in the time series. Black carbon is one of the major air pollutants released during several mining activities having dangerous effect on climate and human health. In this paper we aim to study the behavioral pattern and trends in the time series of black carbon concentration over the three major coal mines of India namely Raniganj, Jharia and Bokaro considering a long term time series data of past 38 years using regression and fractal dimensional analysis of black carbon between the major coal mines with the help statistical tools like Hurst exponent, predictability index and trend percent. In this comparative study it is observed that the time series display anti persistent behavior with positive and large variation then the past time. The results and comparisons obtained will be helpful in studying the behavior and trends in the concentration of black carbon over the coal mines regions. The significance of the study will be helpful to gather the interest of researcher’s, NGO’s and government towards the black carbon concentration over the coal mines so that preventive measures and new policies be framed to keep a check on black carbon concentration in these areas.

Highlights • The study is about the forecasting the deaths because of COVID-19 in major countries around the globe. Its noble study. • It will help the different countries to make the decision on this coronavirus disease. • Wavelet and ARIMA are coupled to develop new hybrid model, which computes accurate prediction with the least error. • The model provides the 99% approximate accuracy. • The manuscript will also help to all for preparing isolation wards and strategy for the newly infected patients., Everywhere around the globe, the hot topic of discussion today is the ongoing and fast-spreading coronavirus disease (COVID-19), which is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). Earlier detected in Wuhan, Hubei province, in China in December 2019, the deadly virus engulfed China and some neighboring countries, which claimed thousands of lives in February 2020. The proposed hybrid methodology involves the application of discreet wavelet decomposition to the dataset of deaths due to COVID-19, which splits the input data into component series and then applying an appropriate econometric model to each of the component series for making predictions of death cases in future. ARIMA models are well known econometric forecasting models capable of generating accurate forecasts when applied on wavelet decomposed time series. The input dataset consists of daily death cases from most affected five countries by COVID-19, which is given to the hybrid model for validation and to make one month ahead prediction of death cases. These predictions are compared with that obtained from an ARIMA model to estimate the performance of prediction. The predictions indicate a sharp rise in death cases despite various precautionary measures taken by governments of these countries.