Browsing by Author "Nadia Gul"

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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)