Analysis of HIV/AIDS Model with risk compensation effects among Pre-Exposure Prophylaxis users and infectious immigrants - Janet Kikelomo Oladejo; Abiodun Adewale Taiwo; Sefiyat Opeyemi Fawale; Temidayo Joseph Oluwafemi (Jambura Journal of Biomathematics (JJBM), 2025)
Pre-Exposure Prophylaxis (PrEP) is a promising HIV prevention strategy,  and its provision has grown rapidly in several  countries,  including those in Sub-Saharan Africa.  However, lingering concerns  remain  that introducing PrEP may  lead  to unintended consequences,  such  as decreased  adherence  to other  prevention methods  and increased  risky sexual  behaviour, culminating in  risk  compensation.  This  study  employs a six-compartment mathematical model  to investigate the effects of risk  compensation behaviour among  PrEP users in a population with  an influx of infectious immigrants. The model  exhibits only  disease-free  equilibrium points  in the absence of  infective immigrants  and  endemic   equilibrium with  the  influx of  infected  immigrants.   The  disease-free equilibrium point  exists and is locally and globally asymptotically stable in the absence of infective immigrants when  the basic reproduction number  is less than one. In contrast, the model  exhibits only  endemic  equilibrium in the presence of infective immigrants, which is asymptotically stable when basic reproduction number  exceeds unity. A sensitivity analysis of the parameters  associated  with  R1 was performed using the normalized forward sensitivity index  to determine  the most influential parameter.   The  analysis revealed  that the number  of sexual partners  had  the greatest  influence   on  disease  endemicity.   Numerical  simulations supported the analytical findings, showing that  risk  compensation undermines PrEP  effectiveness  and  that  multiple sexual  partners increase  new  HIV infections.    However, PrEP can  significantly reduce  new  infections in  a population with varying immigrant influx and  no risk  compensation behaviour, highlighting  its potential  impact  in controlling HIV spread.     The  effectiveness   of  PrEP  depends on  strict  adherence   to  usage   in  combination  with   other preventive measures.  The disease persists  with  the inflow of infective immigrants.