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Numerical Modeling of Fractional‐Order Biological Systems

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  • Fathalla A. Rihan

Abstract

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 ℛ0 (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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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:816803
DOI: 10.1155/2013/816803
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