SZ Rida

Publications (5)0 Total impact

• Source

  Available from: PubMed Central

  Article: Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection.

  Aam Arafa, Sz Rida, M Khalil
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  ABSTRACT: In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.
  Nonlinear Biomedical Physics 01/2012; 6(1):1.
• Article: AAM Arafa, SZ Rida, M Khalil, Solutions of Fractional Order Model of Childhood Diseases with Constant Vaccination Strategy

  AAM Arafa, SZ Rida, M Khalil
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  ABSTRACT: 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.
  Mathematical Sciences Letters. 01/2012; 1.
• Article: Solutions of Fractional Order Model of Childhood Diseases with Constant Vaccination Strategy

  AAM Arafa, SZ Rida, M Khalil
  [show abstract] [hide abstract]
  ABSTRACT: 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.
  Mathematical Sciences Letters (Natural sciences). 01/2012;
• Article: Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection( AAM Arafa, SZ Rida, M Khalil)

  AAM Arafa, SZ Rida, M Khalil
  [show abstract] [hide abstract]
  ABSTRACT: In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.
  Nonlinear Biomedical Physics 01/2012;
• Source

  Available from: Mohamed Khalil

  Article: Fractional Order Model of Human T-cell Lymphotropic Virus I (HTLV-I) Infection of CD4+ T-Cells

  AAM Arafa, SZ Rida, M Khalil
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  ABSTRACT: In this paper, we introduce fractional-order into a model of (HTLV-I) infection of CD 4+ T-cells. Generalized Euler method (GEM) is implemented to give approximate and analytical solutions of the presented problem. The fractional derivatives are described in the Caputo sense.
  Advanced Studies in Biology. 01/2011; Vol. 3(7):347 - 353.