Dynamics of a multi-strain HIV/AIDS epidemic model with treatment and its adherence

This study presents a novel two-strain nonlinear mathematical model to assess the impact of treatment availability and adherence, on the spread of human immunodeficiency virus (HIV) in a community. First, we establish the well-posedness of the proposed model in an epidemiological context. The basic reproduction number for both the strains is determined by the next-generation matrix approach. The local and global analysis of existent equilibrium points using stability and bifurcation theory suggests that the drug-sensitive infected population faces competitive exclusion at lower relative transmission rates of this strain. For higher relative transmission rates of the infection, both infected populations coexist for a long time. The system exhibits transcritical bifurcation and Hopf bifurcation at multiple points with respect to various model parameters. Finally, we validate all the analytical results with an extensive numerical analysis using MATLAB R2023b. In summary, this study provides various conditions for applying different strategies to control the overall disease burden from the system.