Modelling the HIV-TB syndemic: impact of ART coverage and MDR-TB on co-infection dynamics

In this work, we introduce a novel co-infection mathematical model of HIV and MTB infections by combining ART and MDR-TB. The population is divided into eight classes: susceptible individuals (S), HIV-infected (IH), latent TB (LT), active TB (IT), co-infected (IC), MDR-TB cases (IMDR), individuals on ART (A) and recovered individuals (R). The well-posedness and boundedness of the model are established. Stability of the equilibrium points is analyzed via the basic reproduction number and LaSalle's invariance principle. Sensitivity analysis identifies the most influential parameters through numerical and graphical methods. Simulations using the RK4 method illustrate the model's dynamics. Furthermore, the impact of ART scale-up and MDR-TB on HIV, TB and co-infection classes is examined. The results highlight effective strategies, emphasizing ART's role in reducing HIV progression and TB susceptibility, and the importance of MDR-TB. This framework provides insights into the dynamics of co-infection and supports public health interventions.