Browsing by Author "Kumar, Pushpendra"

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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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    Fractional dynamics of 2019-nCOV in Spain at different transmission rate with an idea of optimal control problem formulation
    (Elsevier B.V., 2021-07-29T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Nisar, Kottakkaran Sooppy; Jamshed, Wasim; Mohamed, Mohamed S.
    In this article, we studied the fractional dynamics of the most dangerous deathly disease which outbreaks have been recorded all over the world, called 2019-nCOV or COVID-19. We used the numerical values of the given parameters based on the real data of the 2019-nCOV cases in Spain for the time duration of 25 February to 9 October 2020. We performed our observations with the help of the Atangana-Baleanu (AB) non-integer order derivative. We analysed the optimal control problem in a fractional sense for giving the information on all necessary health care issues. We applied the Predictor-Corrector method to do the important graphical simulations. Also, we provided the analysis related to the existence of a unique solution and the stability of the proposed scheme. The aim and the main contribution of this research is to analyse the structure of novel coronavirus in Spain at different transmission rate and to indicate the danger of this deathly disease for future with the introduction of some optimal controls and health care measures. � 2021
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    Fractional time-delay mathematical modeling of Oncolytic Virotherapy
    (Elsevier Ltd, 2021-06-19T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Yusuf, Abdullahi; Kumar, Sunil
    An emerging treatment tool which uses replication-competent viruses to dissipate cancers without causing deficit to normal tissues, named as oncolytic virotherapy, is discussed in the article. We analysed a fractional delay dynamical model on the oncolytic virotherapy compositing viral lytic cycle and virus-specific cytotoxic T lymphocyte (CTL) response. We used a well known Caputo fractional derivative to analyse the structure of the given dynamical model. Using the literature of fixed-point theory, the given time-delay model is specified to have existence of a unique solution. We established different types of graphical simulations for the various values of R0 and R1. We observed a different behaviour of the given fractional model as compare to the integer order model. The given algorithm is smooth in use and reliable to apply on different delay dynamical models. � 2021 Elsevier Ltd
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    A malaria model with Caputo-Fabrizio and Atangana-Baleanu derivatives
    (World Scientific, 2020-11-02T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Rangaig, Norodin A.; Kumar, Sachin
    In this paper, we study two fractional models in the Caputo-Fabrizio sense and Atangana-Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number R0 is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams-Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order ?. � 2021 World Scientific Publishing Company.
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    A mathematical study of a tuberculosis model with fractional derivatives
    (World Scientific, 2021-02-04T00:00:00) Abboubakar, Hamadjam; Kumar, Pushpendra; Erturk, Vedat Suat; Kumar, Anoop
    In this work, we use a Predictor-Corrector method to implement and derive an iterative solution of an existing Tuberculosis (TB) model with two fractional derivatives, namely, Caputo-Fabrizio fractional derivative and the new generalized Caputo fractional derivative. We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model. Then, we study the global asymptotic stability of disease-free equilibrium of the fractional models. We also prove, for each fractional model, the existence and uniqueness of solutions. An iterative solution of the two models is computed using the Predictor-Corrector method. Using realistic parameter values, we perform numerical simulations for different values of the fractional order. Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo-Fabrizio fractional derivative and the classical integer-order TB model. � 2021 World Scientific Publishing Company.
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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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    On the existence and uniqueness of a nonlinear q -difference boundary value problem of fractional order
    (World Scientific, 2021-09-23T00:00:00) Bekri, Zouaoui; Erturk, Vedat Suat; Kumar, Pushpendra
    In this research collection, we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form cD q?v(t) - h(t,v(t))=0, 0 ? t ? 1, ?1v(0) + ?1Dqv(0)=v(?1),?2v(1) - ?2Dqv(1) = v(?2), where 1 < ? ? 2, (?1,?2) (0, 1)2, ?i,?i ?(i = 1, 2), h C([0, 1] � ?, ?) and cD q? represents the Caputo-type nonclassical q-derivative of order ?. We use well-known principal of Banach contraction, and Leray-Schauder nonlinear alternative to vindicate the unique solution existence of the given problem. Regarding the applications, some examples are solved to justify our outcomes. � 2022 World Scientific Publishing Company.
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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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    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
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    A study on canine distemper virus (CDV) and rabies epidemics in the red fox population via fractional derivatives
    (Elsevier B.V., 2021-05-05T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Yusuf, Abdullahi; Nisar, Kottakkaran Sooppy; Abdelwahab, Sayed F.
    Several deadly epidemics that have recognized as serious problems all over the world in the last few decades. Lassa hemorrhagic fever, coronavirus, dengue fever, malaria, and HIV are well-known deadly diseases in humans. In this research, we analysed the dynamics of the canine distemper virus (CDV) and rabies epidemics in the red fox population of the northern region of Italy with the help of time-fractional models. We performed our analysis in the new generalized Caputo non-classical derivative sense with the application of the Predictor�Corrector algorithm. We used the data of northern Italy for simulations and estimated the endemic equilibrium points for both CDV and rabies models. Also, we presented the local stability of disease-free equilibrium points. Some theorems are mentioned for the purpose of existence and uniqueness analysis. Our results are perfect for giving an idea of the dynamics of the CDV and rabies epidemic in northern Italy. The dynamics of the given solutions are specified with the help of necessary graphical simulations. The projected algorithm is so effective in finding the solutions of complex dynamical systems. By this study, we give an idea of how applied mathematics is directly connected to biological studies. The major scientific aim of this study is to understand the outbreaks of CDV and rabies on the population of the red foxes by using the texture of fractional mathematical models. � 2021 The Authors