Mathematical modelling and analysis of HIV/AIDS and trichomonas vaginalis co-infection

Abstract

Deterministic models for the transmission dynamics of HIV/AIDS and trichomonas vaginalis (TV) in a human population are formulated and analysed. The models which assumed standard incidence formulations are shown to have globally asymptotically stable (GAS) disease-free equilibria whenever their associated reproduction number is less than unity. Furthermore, both models possess a unique endemic equilibrium that is GAS whenever the associated reproduction number is greater than unity. An extended model for the co-infection of TV and HIV in a human population is also designed and rigorously analysed. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed by assuming that the co-infection of individuals with HIV and TV is negligible. Furthermore, in the absence of co-infection, the DFE of the model is shown to be GAS whenever the associated reproduction number is less than unity. This study identifies a sufficient condition for the emergence of backward bifurcation in the model, namely TV-HIV co-infection. The endemic equilibrium point is shown to be GAS (for a special case) when the associated reproduction number is greater than unity. Numerical simulations of the model, using initial and demographic data, show that increased incidence of TV in a population increases HIV incidence in the population. It is further shown that control strategies, such as treatment, condom-use and counselling of individuals with TV symptoms, can lead to the effective control or elimination of HIV in the population if their effectiveness level is high enough.