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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.

Machine learning is an innovative approach that has extensive applications in prediction. This technique needs to be applied for the COVID-19 pandemic to identify patients at high risk, their death rate, and other abnormalities. It can be used to understand the nature of this virus and further predict the upcoming issues. This literature-based review is done by searching the relevant papers on machine learning for COVID-19 from the databases of SCOPUS, Academia, Google Scholar, PubMed, and ResearchGate. This research attempts to discuss the significance of machine learning in resolving the COVID-19 pandemic crisis. This paper studied how machine learning algorithms and methods can be employed to fight the COVID-19 virus and the pandemic. It further discusses the primary machine learning methods that are helpful during the COVID-19 pandemic. We further identified and discussed algorithms used in machine learning and their significant applications. Machine learning is a useful technique, and this can be witnessed in various areas to identify the existing drugs, which also seems advantageous for the treatment of COVID-19 patients. This learning algorithm creates interferences out of unlabeled input datasets, which can be applied to analyze the unlabeled data as an input resource for COVID-19. It provides accurate and useful features rather than a traditional explicitly calculation-based method. Further, this technique is beneficial to predict the risk in healthcare during this COVID-19 crisis. Machine learning also analyses the risk factors as per age, social habits, location, and climate.

The potential of four different neuro-fuzzy embedded meta-heuristic algorithms, particle swarm optimization, genetic algorithm, harmony search, and teaching–learning-based optimization algorithm, was investigated in this study in estimating the water quality of the Yamuna River in Delhi, India. A cross-validation approach was employed by splitting data into three equal parts, where the models were evaluated using each part. The main aim of this study was to find an accurate prediction model for estimating the water quality of the Yamuna River. It is worth noting that the hybrid neuro-fuzzy and LSSVM methods have not been previously compared for this issue. Monthly water quality parameters, total kjeldahl nitrogen, free ammonia, total coliform, water temperature, potential of hydrogen, and fecal coliform were considered as inputs to model chemical oxygen demand (COD). The performance of hybrid neuro-fuzzy models in predicting COD was compared with classical neuro-fuzzy and least square support vector machine (LSSVM) methods. The results showed higher accuracy in COD prediction when free ammonia, total kjeldahl nitrogen, and water temperature were used as inputs. Hybrid neuro-fuzzy models improved the root mean square error of the classical neuro-fuzzy model and LSSVM by 12% and 4%, respectively. The neuro-fuzzy models optimized with harmony search provided the best accuracy with the lowest root mean square error (13.659) and mean absolute error (11.272), while the particle swarm optimization and teaching–learning-based optimization showed the highest computational speed (21 and 24 min) compared to the other models.

The accurate estimation of suspended sediments (SSs) carries significance in determining the volume of dam storage, river carrying capacity, pollution susceptibility, soil erosion potential, aquatic ecological impacts, and the design and operation of hydraulic structures. The presented study proposes a new method for accurately estimating daily SSs using antecedent discharge and sediment information. The novel method is developed by hybridizing the multivariate adaptive regression spline (MARS) and the Kmeans clustering algorithm (MARS–KM). The proposed method’s efficacy is established by comparing its performance with the adaptive neuro-fuzzy system (ANFIS), MARS, and M5 tree (M5Tree) models in predicting SSs at two stations situated on the Yangtze River of China, according to the three assessment measurements, RMSE, MAE, and NSE. Two modeling scenarios are employed, data are divided into 50–50% for model training and testing in the first scenario, and the training and test data sets are swapped in the second scenario. In Guangyuan Station, the MARS–KM showed a performance improvement compared to ANFIS, MARS, and M5Tree methods in term of RMSE by 39%, 30%, and 18% in the first scenario and by 24%, 22%, and 8% in the second scenario, respectively, while the improvement in RMSE of ANFIS, MARS, and M5Tree was 34%, 26%, and 27% in the first scenario and 7%, 16%, and 6% in the second scenario, respectively, at Beibei Station. Additionally, the MARS–KM models provided much more satisfactory estimates using only discharge values as inputs.

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.

Dissolved oxygen (DO) concentration is an important water-quality parameter, and its estimation is very important for aquatic ecosystems, drinking water resources, and agro-industrial activities. In the presented study, a new support vector machine (SVM) method, which is improved by hybrid firefly algorithm–particle swarm optimization (FFAPSO), is proposed for the accurate estimation of the DO. Daily pH, temperature (T), electrical conductivity (EC), river discharge (Q) and DO data from Fountain Creek near Fountain, the United States, were used for the model development. Various combinations of pH, T, EC, and Q were used as inputs to the models to estimate the DO. The outcomes of the proposed SVM–FFAPSO model were compared with the SVM–PSO, SVM–FFA, and standalone SVM with respect to the root mean square errors (RMSE), the mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), and determination coefficient (R2), and graphical methods, such as scatterplots, and Taylor and violin charts. The SVM–FFAPSO showed a superior performance to the other methods in the estimation of the DO. The best model of each method was also assessed in multistep-ahead (from 1- to 7-day ahead) DO, and the superiority of the proposed method was observed from the comparison. The general outcomes recommend the use of SVM–FFAPSO in DO modeling, and this method can be useful for decision-makers in urban water planning and management.

Long-term aerosol climatology is derived using Terra MODIS (Collection 6) enhanced Deep Blue (DB) AOD retrieval algorithm to investigate decadal trend (2006–2015) in columnar aerosol loading, future scenarios and potential source fields over the Indo-Gangetic Plain (IGP), South Asia. Satellite based aerosol climatology was analyzed in two contexts: for the entire IGP considering area weighted mean AOD and for nine individual stations located at upper (Karachi, Multan, Lahore), central (Delhi, Kanpur, Varanasi, Patna) and lower IGP (Kolkata, Dhaka). A comparatively high aerosol loading (AOD: 0.50 ± 0.25) was evident over IGP with a statistically insignificant increasing trend of 0.002 year−1. Analysis highlights the existing spatial and temporal gradients in aerosol loading with stations over central IGP like Varanasi (decadal mean AOD±SD; 0.67 ± 0.28) and Patna (0.65 ± 0.30) exhibit the highest AOD, followed by stations over lower IGP (Kolkata: 0.58 ± 0.21; Dhaka: 0.60 ± 0.24), with a statistically significant increasing trend (0.0174–0.0206 year−1). In contrast, stations over upper IGP reveal a comparatively low aerosol loading, having an insignificant increasing trend. Variation in AOD across IGP is found to be mainly influenced by seasonality and topography. A distinct “aerosol pool” region over eastern part of Ganges plain is identified, where meteorology, topography, and aerosol sources favor the persistence of airborne particulates. A strong seasonality in aerosol loading and types is also witnessed, with high AOD and dominance of fine particulates over central to lower IGP, especially during post-monsoon and winter. The time series analyses by autoregressive integrated moving average (ARIMA) indicate contrasting patterns in randomness of AOD over individual stations with better performance especially over central IGP. Concentration weighted trajectory analyses identify the crucial contributions of western dry regions and partial contributions from central Highlands and north-eastern India, in regulating AOD over stations across IGP. Although our analyses provide some attributes to the observed changes in aerosol loading, we conclude that the spatial and temporal pattern of aerosol properties is highly complex and dynamic over IGP, and require further investigation in order to reduce uncertainty in aerosol-climate model.

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.

Long-term observations and modeling of aerosol loading over the Indo-Gangetic plains (IGP), the Indian desert region and Himalayan slopes are analyzed in the present study. The Box–Jenkins popular ARIMA (AutoRegressive Integrated Moving Average) model was applied to simulate the monthly-mean Terra MODIS (MODerate Resolution Imaging Spectroradiometer) Aerosol Optical Depth (AOD 550 nm) over eight sites in the region covering a period of about 13 years (March 2000–May 2012). The autocorrelation structure has been analyzed indicating a deterministic pattern in the time series that it regains its structure every 24 month period. The ARIMA models namely ARIMA(2,0,12), ARIMA(1,0,6), ARIMA(3,0,0), ARIMA(2,0,13) ARIMA(0,0,12), ARIMA(2,0,2), ARIMA(1,0,12) and ARIMA(0,0,1) have been developed as the most suitable for simulating and forecasting the monthly-mean AOD over the eight selected locations. The Stationary R-squared, R-squared, Root Mean Square Error (RMSE) and Normalized BIC (Bayesian Information Criterion) are used to test the validity and applicability of the developed ARIMA models revealing adequate accuracy in the model performance. The values of Hurst Exponent, Fractal Dimension and Predictability Index for AODs are about 0.5, 1.5 and 0, respectively, suggesting that the AODs in all sites follow the Brownian time-series motion (true random walk). High AOD values (> 0.7) are observed over the industrialized and densely-populated IGP sites associated with low ones over the foothills/slopes of the Himalayas. The trends in AOD during the ~ 13-year period differentiates depending on season and site. During post-monsoon and winter accumulation of aerosols and increasing trends are shown over IGP sites, which are neutralized in pre-monsoon and become slightly negative in monsoon. The AOD over the Himalayan sites does not exhibit any significant trend and seems to be practically unaffected by the aerosol built-up over IGP.

This paper deals with water quality management using statistical analysis and time-series prediction model. The monthly variation of water quality standards has been used to compare statistical mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation at Yamuna River. Model validated using R-squared, root mean square error, mean absolute percentage error, maximum absolute percentage error, mean absolute error, maximum absolute error, normalized Bayesian information criterion, Ljung–Box analysis, predicted value and confidence limits. Using auto regressive integrated moving average model, future water quality parameters values have been estimated. It is observed that predictive model is useful at 95 % confidence limits and curve is platykurtic for potential of hydrogen (pH), free ammonia, total Kjeldahl nitrogen, dissolved oxygen, water temperature (WT); leptokurtic for chemical oxygen demand, biochemical oxygen demand. Also, it is observed that predicted series is close to the original series which provides a perfect fit. All parameters except pH and WT cross the prescribed limits of the World Health Organization /United States Environmental Protection Agency, and thus water is not fit for drinking, agriculture and industrial use.

Statistical analysis of the water quality parameters COD (Chemical Oxygen Demand), BOD (Biochemical Oxygen Demand), DO (Dissolved Oxygen), WT (Water Temperature), AMM (Free Ammonia), TKN (Total Kjeldahl Ni- trogen), TC (Total Coliform), FC (Fecal Coliform) and pH (Potential of Hydrogen) monitored at Hathni Kund Dam (Haryana) Yamuna River in India have been studied. It has been observed that water quality parameter have positive correlation be- tween COD-BOD; AMM-TKN; WT-pH; TC-FC; and negatively correlation between COD-DO; BOD-DO; TKN-FC; DO-WT. Discrete wavelet analyses of water quality parameter using Daubechies wavelet at level 5 have been calculated. It has been observed that the values of signal data at five different levels for AMM, BOD, COD, DO, FC, pH, TC, TKN, WT varies between -1 to 1, -2 to 2, -20 to 20, -2 to 2, -5 to 5, -1 to 1, -2 to 2, -5 to 5, -10 to 10 respectively.