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Nonlinear dynamics and chaos in a fractional-order HIV model. (English) Zbl 1181.37124
Summary: We introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.
MSC:
37N25Dynamical systems in biology
37D45Strange attractors, chaotic dynamics
92C37Cell biology
26A33Fractional derivatives and integrals (real functions)
28A80Fractals