We introduce a fractional order model for the human immunodeficiency virus (HIV) dynamics, where time-varying drug exposure and drug resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug efficacies, and when considering a density-dependent decay rate for the T cells. Other classes of periodic drug efficacies are considered and the effect of the phases of these functions on the dynamics of the model is also studied. The order of the fractional derivative plays an important role in the severity of the epidemics.
Fractional Dynamics of an Infection Model With Time-Varying Drug Exposure
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 14, 2017; final manuscript received November 15, 2017; published online July 26, 2018. Assoc. Editor: Dumitru Baleanu.
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Pinto, C. M. A., and Carvalho, A. R. M. (July 26, 2018). "Fractional Dynamics of an Infection Model With Time-Varying Drug Exposure." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090904. https://doi.org/10.1115/1.4038643
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