Effects of HIV infection on CD4 + T-cell population based on a fractional-order model

Advances in Difference Equations

Dumitru Baleanu¹  Weiping Bu²  Yifa Tang³  Sadia Arshad⁴ 

[1] COMSATS Institute of Information Technology, Lahore, Pakistan;Department of Mathematics, Cankaya University, Ankara, Turkey;Institute of Space Sciences, Magurele-Bucharest, Romania;LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

关键词: fractional derivative;    HIV model;    finite difference scheme;    dynamical analysis;   

DOI  :  10.1186/s13662-017-1143-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY