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Paper

Stability and bifurcations of a minimal model for the effect of PrEP-related risk compensation in epidemics of sexually transmitted infections

Abstract

HIV pre-exposure prophylaxis (PrEP) drastically reduces the risk of HIV infection if taken as prescribed, providing almost perfect protection even during unprotected sexual intercourse. Although this has been transformative in reducing new HIV infections among high-risk populations, it has also been linked to an increase in risk practices -- a phenomenon known as risk compensation -- thereby favoring the spread of other sexually transmitted infections (STIs) deemed less severe. In this paper, we study a minimal compartmental model describing the effect of risk awareness and risk compensation due to PrEP on the spread of other STIs among a high-infection-risk group of men who have sex with men (MSM). The model integrates three key elements of risk-mediated behavior and PrEP programs: (i) HIV risk awareness drives self-protective behaviors (such as condom use and voluntary STI screening); (ii) individuals on PrEP are subject to risk compensation, but (iii) are required to screen for asymptomatic STIs frequently. We derived the basic reproduction number of the system, , and found a transcritical bifurcation at , where the disease-free equilibrium becomes unstable and an endemic equilibrium emerges. This endemic equilibrium is asymptotically stable wherever it exists. We identified critical thresholds in behavioral and policy parameters that separate these regimes and analyzed typical values for plausible parameter choices. Beyond the specific epidemiological context, the model serves as a general framework for studying nonlinear interactions between behavioral adaptation, preventive interventions, and disease dynamics, providing insights into how feedback mechanisms can lead to non-trivial responses in epidemic systems. Finally, our model can be easily extended to study the effect of interventions and risk compensation in other STIs.