Department Of Mathematics And Statistics

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Start date: 2016Subject: search.filters.subject.COVID-19

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    Prediction studies of the epidemic peak of coronavirus disease in Japan: From Caputo derivatives to Atangana-Baleanu derivatives
    (World Scientific, 2021-09-30T00:00:00) Kumar, Pushpendra; Rangaig, Norodin A.; Abboubakar, Hamadjam; Kumar, Anoop; Manickam, A.
    New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo-Fabrizio derivatives, and Atangana-Baleanu derivatives in the Caputo sense. The fixed point theory and Picard-Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order ?, and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals. � 2022 World Scientific Publishing Company.
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    A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives
    (Springer Science and Business Media Deutschland GmbH, 2021-07-20T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Murillo-Arcila, Marina; Banerjee, Ramashis; Manickam, A.
    In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March�03, 2020 to March�29, 2021 which is a data range of more than one complete year. We propose a Atangana�Baleanu type fractional-order model and simulate it by using predictor�corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A�number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper. � 2021, The Author(s).
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    Short-term forecasting of the COVID-19 outbreak in India
    (Oxford University Press, 2021-05-28T00:00:00) Mangla, Sherry; Pathak, Ashok Kumar; Arshad, Mohd; Haque, Ubydul
    As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly spreading in different parts of India, a reliable forecast for the cumulative confirmed cases and the number of deaths can be helpful for policymakers in making the decisions for utilizing available resources in the country. Recently, various mathematical models have been used to predict the outbreak of COVID-19 worldwide and also in India. In this article we use exponential, logistic, Gompertz growth and autoregressive integrated moving average (ARIMA) models to predict the spread of COVID-19 in India after the announcement of various unlock phases. The mean absolute percentage error and root mean square error comparative measures were used to check the goodness-of-fit of the growth models and Akaike information criterion for ARIMA model selection. Using COVID-19 pandemic data up to 20 December 2020 from India and its five most affected states (Maharashtra, Karnataka, Andhra Pradesh, Tamil Nadu and Kerala), we report 15-days-ahead forecasts for cumulative confirmed cases and the number of deaths. Based on available data, we found that the ARIMA model is the best-fitting model for COVID-19 cases in India and its most affected states. � 2021 The Author(s) 2021.
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    A new fractional mathematical modelling of COVID-19 with the availability of vaccine
    (Elsevier B.V., 2021-04-21T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Murillo-Arcila, Marina
    The most dangerous disease of this decade novel coronavirus or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. In this research article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalize it in Atangana�Baleanu derivative sense. The high motivation to apply Atangana�Baleanu fractional derivative on our model is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor�Corrector algorithm to derive the solution of the model. Also, the analysis for the stability of the given algorithm is established. We simulate number of graphs to see the role of vaccine on the dynamics of the population. For practical simulations, we use the parameter values which are based on real data of Spain. The main motivation or aim of this research study is to justify the role of vaccine in this tough time of COVID-19. A clear role of vaccine at this crucial time can be realized by this study. � 2021 The Authors
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    Projections and fractional dynamics of COVID-19 with optimal control strategies
    (Elsevier Ltd, 2021-01-28T00:00:00) Nabi, Khondoker Nazmoon; Kumar, Pushpendra; Erturk, Vedat Suat
    When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers (Rc) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo�Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard�Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved. � 2021