Numerical Modeling of Fractional-Order Biological Systems

Abstract EN

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.