Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model | Zendy

Haiping Ye | Zendy; Yongsheng Ding | Zendy

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Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

Author(s) -

Haiping Ye,

Yongsheng Ding

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/378614

Subject(s) - nonlinear system , chaotic , order (exchange) , predictor–corrector method , fractional calculus , human immunodeficiency virus (hiv) , mathematics , integer (computer science) , epidemic model , statistical physics , physics , computer science , virology , biology , quantum mechanics , finance , artificial intelligence , economics , programming language , population , demography , sociology

We introduce fractional order into an HIV model. We considerthe effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate ofelimination of infected cells by CTLs, based on a fractional-order differentialequation model. For the one-virus model, our analysis shows that the interiorequilibrium which is unstable in the classical integer-order model can becomeasymptotically stable in our fractional-order model and numerical simulationsconfirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using anAdams-type predictor-corrector method

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