Modeling gonorrhea and HIV co-interaction.

A mathematical model was designed to explore the co-interaction of gonorrhea and HIV in the presence of antiretroviral therapy and gonorrhea treatment. Qualitative and comprehensive mathematical techniques have been used to analyse the model. The gonorrhea-only and HIV-only sub-models are first considered. Analytic expressions for the threshold parameter in each sub-model and the co-interaction model are derived. Global dynamics of this co-interaction shows that whenever the threshold parameter for the respective sub-models and co-interaction model is less than unity, the epidemics dies out, while the reverse results in persistence of the epidemics in the community. The impact of gonorrhea and its treatment on HIV dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics co-exists whenever their reproduction numbers exceed unity (with no competitive exclusion). Further, simulations of the full HIV-gonorrhea model also suggests that an increase in the number of individuals infected with gonorrhea (either singly or dually with HIV) in the presence of treatment results in a decrease in gonorrhea-only cases, dual-infection cases but increases the number of HIV-only cases.