Understanding Drug Resistance of HIV Infection with Multidrug Treatment and Immune Response

In the present study, a twin-strain mathematical model comprising drug sensitive (wild type) and drug resistant (mutant) strains is proposed for the dynamics of HIV (Human Immunodeficiency Virus). The purpose is to investigate strategies in the multidrug treatment of HIV infection in the presence of drug resistant strains. The HIV infection dynamics is described by a system of nonlinear differential equations, which governs the interaction of uninfected CD4+ T-cells with free virus. The division of infected cells into pre and post-RT classes has been incorporated into the system to explain the biological steps between the viral infection of CD4+ T-cells and production of HIV virions. Further, a combined drug therapy consisting of Fusion Inhibitor (FI), Reverse Tanscriptase Inhibitor (RTI), and Protease Inhibitor (PI) is introduced into the system so as to reduce viral load and thus increase the T-cell population. Continuous viral replication in the presence of drug therapy results in the emergence of variants of drug resistant virus. Thus, there would not be a complete eradication of virus which enhances the risk of the progression of the disease towards AIDS. The system takes into account this fact by introducing the two types of viral strains- drug sensitive and drug resistant strain. The impact of immune response is also considered on this twin-strain model with multidrug treatment. The stability of the steady states emerging in the system is analysed. Conditions are obtained for stability and existence of uninfected and infected steady states. Results from numerical simulations are exhibited to illustrate the dynamic relationship between multidrug therapy administration, the prevalence of drug resistance, the total level of viral production, and the strength of immune response.