Browsing by Author "Arafa, AAM"

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    Approximate analytical solution of the fractional epidemic model
    (International Journal of Applied Mathematical Research, 2012) Rida, SZ; Abdel Rady, AS; Arafa, AAM; Khalil, M
    In this paper an analytical expression for the solution of the fractional order epidemic model of a non-fatal disease in a population which is assumed to have a constant size over the period of the epidemic is presented. Homotopy analysis method (HAM) is implemented to give approximate and analytical solutions of the presented problem.
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    The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order mode
    (ELSEVIER, 2013) Arafa, AAM; Rida, SZ; Khalil, M
    In this paper, generalized Euler method (GEM) and homotopy analysis method (HAM) are performed to solve the problem of the population dynamics of the human immunodeficiency type 1 virus (HIV-1). We introduce fractional orders to the model of HIV-1 whose components are plasma densities of uninfected CD4+ T-cells, the infected such cells and the free virus. The effect of the drug treatment of HIV-1 will be discussed in this paper.
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    The effect of the environmental parameter on the Hantavirus infection through a fractional-order SI model
    (International Journal of Basic and Applied Sciences,, 2012) Rida, SZ; Abdel Rady, AS; Arafa, AAM; Khalil, M
    In this paper, fractional-order model of the Hantavirus infection in terms of simple differential equations involving the mice population is presented. A study of the effect of changes in ecological conditions and diversity of habitats can be observed by varying the value of the environmental parameter . Generalized Euler method (GEM) is considered in this paper to obtain an analytic approximate solution of this model.
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    THE EFFECT OF VACCINATION ON THE DYNAMICS OFCHILDHOOD DISEASES DESCRIBED BY A FRACTIONAL SIREPIDEMIC MODEL
    (International Journal Of Advanced in Science and Technology, 2012) Rida, SZ; Abd El Radi, AS; Arafa, AAM; Khalil, M
    Childhood vaccination programs have had a dramatic impact onreducing child mortality worldwide. We introduce fractional-order into A SIRmodel that monitors the temporal dynamics of a childhood disease in the pres-ence of preventive vaccine is presented in this paper. Generalized Euler method(GEM) is considered in this paper to obtain an analytic approximate solutionof this model. The obtained results proved that the disease will persist withinthe population if the vaccination coverage level is below a certain threshold.
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    A fractional-order model of HIV infection with drug therapy effect
    (Elsevier, 2014) Arafa, AAM; Rida, SZ; Khalil, M
    In this paper, the fractional-order model that describes HIV infection of CD4+ T cells with therapy effect is given. Generalized Euler Method (GEM) is employed to get numerical solution of such problem. The fractional derivatives are described in the Caputo sense.
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    Numerical behavior of a fractional order dynamical model of RNA silencing
    (International Journal of Scientific World, 2016) El-Sayed, AMA; Khalil, M; Arafa, AAM; Sayed, Amaal
    A class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.
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    Solutions of Fractional Order Model of Childhooddiseases withConstant Vaccination Strategy
    (Math. Sci. Lett, 2012) Arafa, AAM; Rida, SZ; Khalil, M
    Childhood vaccination programs have had a dramatic impact on child morbidity and mortality. Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. We introduce fractional-order into the presented model. Homotopy analysis method (HAM) is considered in this paper to obtain an analytic approximate solution of this model. The results obtained by HAM are compared with the classical fourth order Runge–Kutta method (RK4) to gauge its effectiveness. The obtained results proved that the disease will persist within the population if the vaccination coverage level is below a certain threshold