Dynamics of a two-group model for assessing the impacts of pre-exposure prophylaxis, testing and risk behaviour change on the spread and control of HIV/AIDS in an MSM population

Although much progress has been made in reducing the public health burden of the human immunodeficiency virus (HIV), which causes acquired immunodeficiency syndrome (AIDS), since its emergence in the 1980s (largely due to the large-scale use and availability of potent antiviral therapy, improved diagnostic and intervention and mitigation measures), HIV remains an important public health challenge globally, including in the United States. This study is based on the use of mathematical modeling approaches to assess the population-level impact of pre-exposure prophylaxis (PrEP), voluntary testing (to detect undetected HIV-infected individuals), and changes in human behavior (with respect to risk structure), on the spread and control of HIV/AIDS in an MSM (men-who-have sex-with-men) population. Specifically, a novel two-group mathematical model, which stratifies the total MSM population based on risk (low or high) of acquisition of HIV infection, is formulated. The model undergoes a PrEP-induced backward bifurcation when the control reproduction number of the model is less than one if the efficacy of PrEP to prevent a high-risk susceptible MSM individual from acquiring HIV infection is not perfect (the consequence of which is that, while necessary, having the reproduction number of the model less than one is no longer sufficient for the elimination of the disease in the MSM population). For the case where the efficacy of PrEP is perfect, this study shows that the disease-free equilibrium of the two-group model is globally-asymptotically stable when the associated control reproduction number of the model is less than one. Global sensitivity analysis was carried out to identify the main parameters of the model that have the highest influence on the value of the control reproduction number of the model (thereby, having the highest influence on the disease burden in the MSM population). Numerical simulations of the model, using a plausible range of parameter values, show that if half of the MSM population considered adhere strictly to the specified PrEP regimen (while other interventions are maintained at their baseline values), a reduction of about 22% of the new yearly HIV cases recorded at the peak of the disease could be averted (compared to the worst-case scenario where PrEP-based intervention is not implemented in the MSM population). The yearly reduction at the peak increases to about 50% if the PrEP coverage in the MSM population increases to 80%. This study showed, based on the parameter values used in the simulations, that the prospects of elimination of HIV/AIDS in the MSM community are promising if high-risk susceptible individuals are no more than 15% more likely to acquire HIV infection, in comparison to their low-risk counterparts. Furthermore, these prospects are significantly improved if undetected HIV-infected individuals are detected within an optimal period of time.