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All Journal Jambura Journal of Biomathematics (JJBM) TRANSPUBLIKA INTERNATIONAL RESEARCH IN EXACT SCIENCES (TIRES)
Taiwo, Abiodun Adewale
Unknown Affiliation
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Physics

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Stability and Sensitivity Analysis of HIV/AIDS Model with Saturated Incidence Rate Odebiyi, Olusola Akintunde; Oladejo, Janet Kikelomo; Wasiu Omotayo, Salahu; Taiwo, Abiodun Adewale; Ayanrinola, Olusola Wumi
TRANSPUBLIKA INTERNATIONAL RESEARCH IN EXACT SCIENCES Vol. 4 No. 2 (2025): APRIL
Publisher : Transpublika Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55047/tires.v4i2.1650

Abstract

HIV/AIDS, an extremely harmful sexually transmitted disease, has had a significant impact on worldwide health, establishing itself as one of the most lethal epidemics ever recorded. In this study, a mathematical model is used to analyze how HIV/AIDS spreads and grows, taking into account high incidence rates. The model uses a set of typical differential equations to group people into different categories based on their health status, including those who are vulnerable, those who have been vaccinated, those who are asymptomatic, those who are symptomatic, and those who have AIDS. The effectiveness of the solution indicates that the model is clearly outlined and has important implications for epidemiology. By utilizing the next-generation matrix method, we calculated the basic reproduction number. In order to evaluate the model's stability, a comprehensive examination was conducted on both the local and global stability of both the disease-free and endemic equilibrium points. This analysis provides a comprehensive understanding of the model’s behavior, shedding light on the conditions necessary for the disease to persist or die out. Numerical simulations focusing on these key parameters demonstrate that achieving a disease-free environment is attainable, albeit requiring targeted interventions to maintain stability. This study underscores the significance of understanding saturated incidence rates in modeling HIV/AIDS transmission dynamics. The results offer important information for policymakers and public health authorities, allowing them to create successful tactics for managing the transmission of HIV/AIDS.
Analysis of HIV/AIDS Model with risk compensation effects among Pre-Exposure Prophylaxis users and infectious immigrants Oladejo, Janet Kikelomo; Taiwo, Abiodun Adewale; Fawale, Sefiyat Opeyemi; Oluwafemi, Temidayo Joseph
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 4: December 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i4.30812

Abstract

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.
Co-Authors Ayanrinola, Olusola Wumi Fawale, Sefiyat Opeyemi Odebiyi, Olusola Akintunde Oladejo, Janet Kikelomo Oluwafemi, Temidayo Joseph Wasiu Omotayo, Salahu