A mathematical model of HIV transmission between commercial sex workers and injection drug users

HIV infection remains a global public health problem. Infections arising from commercial sex workers and injection drug users continue to fuel further spread of HIV, hence threatening Kenya's Vision 2030 of achieving zero new HIV infections. In an attempt to study the transmission trend between these two risk groups, a deterministic model for the spread of HIV is formulated. The model is designed in such a way that it allows for free transition between the risk groups. The basic reproduction number is derived. The existence of a transcritical bifurcation and a possible saddle-node bifurcation is shown. The epidemiological consequence of a backward bifurcation is that the classical requirement of having the reproduction number less than unity, while necessary, is no longer sufficient for disease elimination from the population. It is further shown that in the absence of drug user saturation, the model does not exhibit this phenomenon. Numerical simulations show that an increase in the PrEP uptake leads to a decline in the number of HIV patients under ART. Thus, a combination of PrEP uptake and ART would reduce the spread of the disease appreciably. These findings can guide the policy makers on development of effective strategies aimed at limiting and eventual elimination of the spread of HIV.