On the fractional-order model of HIV-1 infection of CD4⁺ T-cells under the influence of antiviral drug treatment

In this article, the fractional-order model, namely HIV-1 infection of CD4⁺ T-cells combined with the effect of antiviral drug treatment, is investigated. The model includes three unknown factors, (i) the uninfected CD4⁺ T-cells, (ii) the infected CD4⁺ T-cells, and (iii) the density of virions in the plasma. The most effective techniques such as the variation-of-parameters method, the variational iteration method, the homotopy perturbation method and the adomian decomposition method are implemented to tackle the mathematical models of Caputo’s fractional derivative. Graphical illustration and numerical results are presented to show the validity and accuracy of the obtained results. It is found that the fractional-order model can be easily solved by means of analytical approaches with less computational cost and the HPM technique is slightly better than others. It is also perceived that the fractional-order approximate solutions can get closer to classical approximate solutions when (Formula presented.).