Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection

Abstract

In this paper, a combined drug treatment for the Human Immunodeficiency Virus (HIV) infection is studied using fractional order differential equations. The fractional order model is considered in the governing equations to account for the memory property on the infection dynamics. The model possesses two different Anti Retro Viral (ARV) drug therapies such as Reverse Transcriptase Inhibitor (RTI) and Protease Inhibitor (PI) that influence the HIV infection spread rate. Spectral collocation method is applied to study the model computationally. Here, different scenarios of treatment regimes for HIV are analysed for three different cases such as (i) No drug therapy is administered; (ii) Single therapy is administered (either RTI and PI) and (iii) the combined therapy (both RTI and PI) is administered. It is found that single PI therapy eradicates virus particles at a higher rate compared to single RTI therapy. In the case of combined therapy, when higher dosage of PI with moderate dosage of RTI is administered, the virus particles are cleared at a higher rate compared to the reversed dosage. The detailed computational analysis and the results obtained are presented in the form of tables and figures.