HIV/AIDS dynamics: Impact of economic classes with transmission from poor clinical settings

We formulate and analyze a nonlinear deterministic HIV/AIDS model with two social classes, namely the poor and the rich including transmission from poor clinical settings with a randomly variable population. Four sub-models are derived from the full model, the disease threshold parameters are computed, and it is shown that the disease will die down if these initial threshold parameters are less than unity and will persist if they exceed unity. The impact of economic classes (along with transmission from poor/inadequate clinical settings) on the disease dynamics is assessed, and we observe that even with a single sexual partner, the reproduction number is slightly greater than unity, implying that the additional transmission can only be from clinical settings. Stability (local and global) of both the disease-free and endemic equilibria are then investigated using various techniques of dynamical systems such as Centre Manifold theory and Lyapunov's second method. Analysis on the bifurcation parameter is carried out to assess the impact of related HIV transmission from poor clinical settings. We estimate some of the model parameter values and numerical simulations of the model are represented graphically. Our results show that the prevalence of HIV in rich communities seems to be higher than that in the poor, but the disease develops faster in impoverished individuals.