Browsing by Author "Anwar Zeb"

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    A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms
    (Elsevier B.V., 2022) Anwar Zeb; Pushpendra Kumar; Vedat Suat Erturk; Thanin Sitthiwirattham; P. Kumar; Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab, 151001, India; email: kumarsaraswatpk@gmail.com
    The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions, and local stability analysis. Furthermore, the unique solution existence for the proposed fractional-order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allows to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how vaccine availability plays an important role in the control of COVID-19 infection. © 2022 The Author(s)
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    Analysis of a discrete mathematical COVID-19 model
    (Elsevier B.V., 2021) Thanin Sitthiwirattham; Anwar Zeb; Saowaluck Chasreechai; Zohreh Eskandari; Mouhcine Tilioua; Salih Djilali; S. Djilali; Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria; email: s.djilali@univ-chlef.dz
    To describe the main propagation of the COVID-19 and has to find the control for the rapid spread of this viral disease in real life, in current manuscript a discrete form of the SEIR model is discussed. The main aim of this is to describe the viral disease in simplest way and the basic properties that are related with the nature of curves for susceptible and infected individuals are discussed here. The elementary numerical examples are given by using the real data of India and Algeria. © 2021 The Author(s)
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    COVID-19 MODELLING WITH SQUARE ROOT SUSCEPTIBLE-INFECTED INTERACTION
    (Serbian Society of Heat Transfer Engineers, 2023) Nadia Gul; Anwar Zeb; Salih Djilali; Mazz Ullah; Zohreh Eskandari; Thitiporn Linitda; A. Zeb; Department of Mathematics, COMSATS University Islamabad, Abbottabad, Pakistan; email: thitiporn_lin@dusit.ac.th; T. Linitda; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand; email: anwar@cuiatd.edu.pk
    We propose a COVID-19 mathematical model related to functional shape with square root susceptible-infected interaction. Using the Hurwitz criterion and then a graph theoretical-method for the construction of a Lyapunov function, we discuss both local and global stability. The analytical solution of the system is obtained in a special case. A non-standard finite difference scheme is then developed with the aim to obtain a proper discrete-time version of the model. Simulations show a good agreement between the proposed discretization and the results given by standard numerical methods. © 2023 Society of Thermal Engineers of Serbia Published by the Vin_a Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions
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    Dynamical bifurcation of a sewage treatment model with general higher-order perturbation
    (Elsevier B.V., 2022) Yassine Sabbar; Anwar Zeb; Driss Kiouach; Nadia Gul; Thanin Sitthiwirattham; Dumitru Baleanu; Jiraporn Pongsopa; A. Zeb; Department of Mathematics, COMSATS University of Islamabad, Abbottabad Campus, Abbottabad, Khyber Pakhtunkhwa, Pakistan; email: anwar@cuiatd.edu.pk
    In this research, we expose new results on the dynamics of a high disturbed chemostat model for industrial wastewater. Due to the complexity of heavy and erratic environmental variations, we take into consideration the polynomial perturbation. We scout the asymptotic characterization of our proposed system with a general interference response. It is demonstrated that the long-run characteristics of the chemostat process are classified by using the threshold classification approach. If the critical sill is strictly negative, the bacteria will disappear exponentially, indicating that the chemostat wastewater process is not running (excluded scenario), otherwise, the stationarity and ergodicity properties of our model are verified (practical scenario). The theoretical arsenal of this work offers a comprehensive overview of the industrial wastewater behavior under general hypotheses and introduces novel technical aspects to deal with other perturbed systems in biology. Numerically, we audit the accuracy of our threshold in three particular situations: linear, quadratic and cubic perturbations. We establish that the increasing order of disturbance has a passive influence on the extinction time of bacteria. This finding highlights that complex noise sources fulfill a significant role in the transient dynamics of chemostat systems. © 2022 The Author(s)
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    Semi-analytical solutions for fuzzy caputoÐfabrizio fractional-order two-dimensional heat equation
    (MDPI, 2021) Thanin Sitthiwirattham; Muhammad Arfan; Kamal Shah; Anwar Zeb; Salih Djilali; Saowaluck Chasreechai; A. Zeb; Department of Mathematics, Abbotabad Campus, COMSATS University of Islamabad, Khyber Pakhtunkhwa, 22060, Pakistan; email: anwar@cuiatd.edu.pk
    In the analysis in this article, we developed a scheme for the computation of a semi-analytical solution to a fuzzy fractional-order heat equation of two dimensions having some external diffusion source term. For this, we applied the Laplace transform along with decomposition tech-niques and the Adomian polynomial under the CaputoÐFabrizio fractional differential operator. Furthermore, for obtaining a semi-analytical series-type solution, the decomposition of the unknown quantity and its addition established the said solution. The obtained series solution was calculated and approached the approximate solution of the proposed equation. For the validation of our scheme, three different examples have been provided, and the solutions were calculated in fuzzy form. All the three illustrations simulated two different fractional orders between 0 and 1 for the upper and lower portions of the fuzzy solution. The said fractional operator is nonsingular and global due to the presence of the exponential function. It globalizes the dynamical behavior of the said equation, which is guaranteed for all types of fuzzy solution lying between 0 and 1 at any fractional order. The fuzziness is also included in the unknown quantity due to the fuzzy number providing the solution in fuzzy form, having upper and lower branches. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.