Yazar "Khan, Amir" 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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    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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    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.
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    Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model
    (Elsevier, 2021) Hussain, Ghulam; Khan, Tahir; Khan, Amir; Inc, Mustafa; Zaman, Gul; Nisar, Kottakkaran Sooppy; Akgul, Ali
    Novel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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    Stochastic COVID-19 SEIQ epidemic model with time-delay
    (Elsevier, 2021) Khan, Amir; Ikram, Rukhsar; Din, Anwarud; Humphries, Usa Wannasingha; Akgul, Ali
    In this work, we consider an epidemic model for corona-virus (COVID-19) with random perturbations as well as time delay, composed of four different classes of susceptible population, the exposed population, the infectious population and the quarantine population. We investigate the proposed problem for the derivation of at least one and unique solution in the positive feasible region of non-local solution. For one stationary ergodic distribution, the necessary result of existence is developed by applying the Lyapunov function in the sense of delay-stochastic approach and the condition for the extinction of the disease is also established. Our obtained results show that the effect of Brownian motion and noise terms on the transmission of the epidemic is very high. If the noise is large the infection may decrease or vanish. For validation of our obtained scheme, the results for all the classes of the problem have been numerically simulated.