Dynamics of HIV among sex workers and injecting drug users

HIV infection is a serious public-health challenge globally, and sex workers and injecting drug users (IDUs) are among the populations at greatest risk of transmission. In this paper, we formulate and analyze a deterministic mathematical model with five compartments, the Susceptible-HIV-infectious-AIDS (SHA) model, which simultaneously incorporates sexual and injection-related modes of transmission, behavioral change, public health education, and migration between the sex worker and injecting drug user subpopulations. The basic reproduction number R 0 is derived in closed form using the next-generation matrix approach. The existence of a disease-free equilibrium (DFE) and an endemic equilibrium (EE) are established. Local and global stability results in terms of R 0 are proved using the Routh-Hurwitz criterion and the Castillo-Chavez global-stability technique. A normalized forward sensitivity analysis points out the parameters that most strongly influence R 0 , and fourth-order Runge–Kutta numerical simulations show the transient dynamics of the two sub-populations as they progress toward the endemic state. For the considered parameter set, R 0 = 1.1866 > 1 , the DFE is unstable, and the disease persists, with recruitment rates and effective contact rates being the strongest amplifiers of R 0 , and natural mortality, disease-induced mortality, behavioral modification, and public-health education being the strongest suppressors. Such findings provide specific, ordered intervention targets condom promotion, needle-exchange/behaviour-change programs and public-health education for lowering HIV transmission among these interconnected critical populations.