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Abstract
In this paper, we study the HIV infection model based on fractional derivative with particular focus on the degree of T-cell depletion that can be caused by viral cytopathicity. The arbitrary order of the fractional derivatives gives an additional degree of freedom to fit more realistic levels of CD4+ cell depletion seen in many AIDS patients. We propose an implicit numerical scheme for the fractional-order HIV model using a finite difference approximation of the Caputo derivative. The fractional system has two equilibrium points, namely the uninfected equilibrium point and the infected equilibrium point. We investigate the stability of both equilibrium points. Further we examine the dynamical behavior of the system by finding a bifurcation point based on the viral death rate and the number of new virions produced by infected CD4+ T-cells to investigate the influence of the fractional derivative on the HIV dynamics. Finally numerical simulations are carried out to illustrate the analytical results.
Highlights
According to WHO there were approximately million people at the end of living with HIV with . million people becoming newly infected in globally with HIV
The advantage of the generalized model is that the fractional-order system possesses memory, which belongs to the main features of the immune response
An implicit numerical scheme has been proposed for the fractional-order HIV model using a finite difference approximation of the Caputo derivative
Summary
According to WHO there were approximately million people at the end of living with HIV with . million people becoming newly infected in globally with HIV. Much work has done on modeling the HIV infection with fractional-order derivatives [ – ] and [ ]. In [ ] a fractional-order time-delay model is investigated which include three types of cells, namely healthy CD + T-cells, infected CD + T-cells and free HIV virus particles.
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