Mathematics And Statistics - Research Publications
Permanent URI for this collectionhttps://kr.cup.edu.in/handle/32116/47
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Item Fractional time-delay mathematical modeling of Oncolytic Virotherapy(Elsevier Ltd, 2021-06-19T00:00:00) Kumar, Pushpendra; Erturk, Vedat Suat; Yusuf, Abdullahi; Kumar, SunilAn 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 LtdItem 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 AuthorsItem 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, MarinaThe 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 AuthorsItem 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 SuatWhen 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