Yazar "Zarin, Rahat" seçeneğine göre listele

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    Deterministic and fractional modeling of a computer virus propagation
    (Elsevier, 2022) Zarin, Rahat; Khaliq, Hammad; Khan, Amir; Khan, Dolat; Akgul, Ali; Humphries, Usa Wannasingha
    The dynamic behaviors of computer virus models are investigated. In the first phase, we discussed the deterministic version of the proposed model by taking into consideration the local and global stability. For global stability the Castillo-Chavez approach is taken into account. The deterministic version is numerically solved by the Runge-Kutta scheme. The model is then fractionalized by using the Atangana-Baleanu-Caputo operator. Existence uniqueness and Hyers-Ulam stability of the fractionalized model is established. The Atangana-Toufik method is used for the numerical examination of a fractional version of the proposed model.
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    Öğe
    Fractional modeling of COVID-19 pandemic model with real data from Pakistan under the ABC operator
    (Amer Inst Mathematical Sciences-Aims, 2022) Zarin, Rahat; Khan, Amir; Aurangzeb; Akgul, Ali; Akgul, Esra Karatas; Humphries, Usa Wannasingha
    In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.
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    Öğe
    Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
    (Springer, 2021) Khan, Amir; Zarin, Rahat; Humphries, Usa Wannasingha; Akgul, Ali; Saeed, Anwar; Gul, Taza
    In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik-Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.