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2013 Numerical Modeling of Fractional-Order Biological Systems
Fathalla A. Rihan
Abstr. Appl. Anal. 2013(SI25): 1-11 (2013). DOI: 10.1155/2013/816803


We provide a class of fractional-order differential models of biological systems with memory, such as dynamics of tumor-immune system and dynamics of HIV infection of CD4+ T cells. Stability and nonstability conditions for disease-free equilibrium and positive equilibria are obtained in terms of a threshold parameter 0 (minimum infection parameter) for each model. We provide unconditionally stable method, using the Caputo fractional derivative of order α and implicit Euler’s approximation, to find a numerical solution of the resulting systems. The numerical simulations confirm the advantages of the numerical technique and using fractional-order differential models in biological systems over the differential equations with integer order. The results may give insight to infectious disease specialists.


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Fathalla A. Rihan. "Numerical Modeling of Fractional-Order Biological Systems." Abstr. Appl. Anal. 2013 (SI25) 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095387
MathSciNet: MR3090284
Digital Object Identifier: 10.1155/2013/816803

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI25 • 2013
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