{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T18:08:33Z","timestamp":1788804513604,"version":"build-2803163510"},"reference-count":46,"publisher":"L and H Scientific Publishing, LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JAND"],"published-print":{"date-parts":[[2027,3,1]]},"abstract":"<jats:p>Since the 1980s, HIV\/AIDS has evolved from an acute epidemic into a manageable chronic condition, yet approximately 39 million people worldwide live with HIV, highlighting persistent gaps in epidemic control. In this research work, We develop a compartmental model of HIV\/AIDS transmission incorporating pre-exposure prophylaxis (PrEP), post-exposure prophylaxis (PEP), condom usage, and antiretroviral treatment (ART). Mathematical analysis shows local asymptotic stability when the basic reproduction number (R_{0H}) &lt; 1. The model exhibits backward bifurcation with imperfect prophylaxis, where endemic states persist even when R_{0H} &lt; 1; this vanishes at 100% efficacy. Sensitivity analysis identified natural death rate, HIV-to-AIDS progression, contact rate, and AIDS-to-treatment progression as most influential parameters. Calibrated with South African data (2010-2023), the model predicts 28% reduction in new infections by 2033. Simulations show that high condom efficacy (&gt;80\\%) combined with PrEP, PEP, and ART could reduce transmission by 75%, demonstrating the effectiveness of integrated prevention strategies.<\/jats:p>","DOI":"10.5890\/jand.2027.03.011","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:41:02Z","timestamp":1788802862000},"page":"211-265","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Analysis of HIV\/AIDS by Incorporating the Usage of Condoms, Prophylaxis and Antiretroval Drugs as Intervention Measures"],"prefix":"10.5890","volume":"16","author":[{"given":"G. O.","family":"Acheneje","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Abraham","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.O.","family":"Omale","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"W.","family":"Atokolo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B.","family":"Bolaji","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"7015","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"ref1","unstructured":"[1] UNAIDS (2023), Global HIV & AIDS statistics - Fact sheet. https:\/\/www.unaids.org\/en\/resources\/fact-sheet."},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"[2] Ward, A.R., Mota, T.M., and Jones, R.B. (2021), Immunological approaches to HIV cure, Seminars in Immunology, 51, 101412.","DOI":"10.1016\/j.smim.2020.101412"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"[3] Granelli-Piperno, A., Delgado, E., and Finkel, V. (1998), Immature dendritic cells selectively replicate macrophagetropic (M-tropic) human immunodeficiency virus type 1, while mature cells efficiently transmit both M- and T-tropic virus, Journal of Virology, 72(4), 2733-2737.","DOI":"10.1128\/JVI.72.4.2733-2737.1998"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"[4] Miller, V., Mocroft, A., Reiss, P., and Katlama, C. (1999), Relations among CD4 lymphocyte count nadir, antiretroviral therapy, and HIV-1 disease progression: results from the EuroSIDA study, Annals of Internal Medicine, 130(7), 570-577.","DOI":"10.7326\/0003-4819-130-7-199904060-00005"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"[5] van Heuvel, Y., Schatz, S., Rosengarten, J.F., and Stitz, J. (2022), Infectious RNA: human immunodeficiency virus (HIV) biology, therapeutic intervention, and the quest for a vaccine, Toxins, 14(2), 138.","DOI":"10.3390\/toxins14020138"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"[6] Patel, P., Borkowf, C.B., Brooks, J.T., Lasry, A., Lansky, A., and Mermin, J. (2014), Estimating per-act HIV transmission risk: a systematic review, AIDS, 28(10), 1509-1519.","DOI":"10.1097\/QAD.0000000000000298"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"[7] Eisinger, R.W., Dieffenbach, C.W., and Fauci, A.S. (2019), HIV viral load and transmissibility of HIV infection: undetectable equals untransmittable, JAMA, 321(5), 451-452.","DOI":"10.1001\/jama.2018.21167"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"[8] Piot, P. and Laga, M. (1989), Genital ulcers, other sexually transmitted diseases, and the sexual transmission of HIV, BMJ, 298(6674), 623-624.","DOI":"10.1136\/bmj.298.6674.623"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"[9] Grant, R.M., Lama, J.R., Anderson, P.L., McMahan, V., Liu, A., Vargas, L., and Buchbinder, S.P. (2010), Preexposure chemoprophylaxis for HIV prevention in men who have sex with men, The New England Journal of Medicine, 363(27), 2587-2599.","DOI":"10.1056\/NEJMoa1011205"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"[10] Cohen, A., Mathiasen, V.D., Sch\u00f6n, T., and Wejse, C. (2019), The global prevalence of latent tuberculosis: a systematic review and meta-analysis, European Respiratory Journal, 54(3), 1900655.","DOI":"10.1183\/13993003.00655-2019"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"[11] INSIGHT START Study Group (2015), Initiation of antiretroviral therapy in early asymptomatic HIV infection, The New England Journal of Medicine, 373(9), 795-807.","DOI":"10.1056\/NEJMoa1506816"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"[12] Beyrer, C., Bekker, L.G., Pozniak, A., and Barr\u00e9-Sinoussi, F. (2016), Pre-exposure prophylaxis works - it's time to deliver, The Lancet, 387(10013), 1482-1484.","DOI":"10.1016\/S0140-6736(15)60724-3"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"[13] Scanlon, M.L. and Vreeman, R.C. (2013), Current strategies for improving access and adherence to antiretroviral therapies in resource-limited settings, HIV\/AIDS - Research and Palliative Care, 5, 1-17.","DOI":"10.2147\/HIV.S28912"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"[14] Odiba, P., Acheneje, G.O., and Bolaji, B. (2024), A compartmental deterministic epidemiological model with non-linear differential equations for analyzing the co-infection dynamics between COVID-19, HIV, and monkeypox diseases, Healthcare Analytics, 5, 100311.","DOI":"10.1016\/j.health.2024.100311"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"[15] Atokolo, W., Acheneje, G.O., and Bolaji, B. (2024), Fractional mathematical model for the transmission dynamics and control of Lassa fever, Franklin Open, 7, 100110.","DOI":"10.1016\/j.fraope.2024.100110"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"[16] Bolaji, B., Acheneje, G.O., and Odiba, P. (2024b), Dynamical analysis of HIV-TB co-infection transmission model in the presence of treatment for TB, Bulletin of Biomathematics, 2, 21-56.","DOI":"10.59292\/bulletinbiomath.2024002"},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"[17] Omame, A., Atokolo, W., and Onyilo, F.O. (2024), Understanding the impact of HIV on mpox transmission in the MSM population: a mathematical modeling study, Infectious Disease Modelling, 9(4), 1117-1137.","DOI":"10.1016\/j.idm.2024.05.008"},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"[18] Tigabu, K.A., Doungmo Goufo, E.F., and Mugisha, S. (2021), Mathematical modeling of HIV\/AIDS with optimal control: a case study in Ethiopia, Results in Physics, 26, 104263.","DOI":"10.1016\/j.rinp.2021.104263"},{"key":"ref19","doi-asserted-by":"crossref","unstructured":"[19] Arias, R., De Angeles, K., Maleki, S., and Ahangar, R.R. (2022), Mathematical modeling of the HIV-AIDS epidemic, Open Access Library Journal, 9, 1-15.","DOI":"10.4236\/oalib.1107972"},{"key":"ref20","unstructured":"[20] Ogunmodimu, M.O., Bolaji, B., and Atokolo, W. (2024), A mathematical model for the prevention of HIV\/AIDS in the presence of undetectable equals untransmittable viral load, International Journal of Mathematical Sciences and Optimization, 10(2), 36-57."},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"[21] Zanib, S.A., Ramzan, S., and Shah, M.A. (2024), Comprehensive analysis of mathematical model of HIV\/AIDS incorporating fisher-folk community, Modeling Earth Systems and Environment, 10, 6323-6340.","DOI":"10.1007\/s40808-024-02099-9"},{"key":"ref22","doi-asserted-by":"crossref","unstructured":"[22] Bolaji, B., Acheneje, G.O., and Atokolo, W. (2024a), A model for the control of transmission dynamics of human monkeypox disease in Sub-Saharan Africa, Journal of the Nigerian Society of Physical Sciences, 1800.","DOI":"10.46481\/jnsps.2024.1800"},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"[23] Acheneje, G.O., Atokolo, W., and Bolaji, B. (2024), Modeling the transmission dynamics of the co-infection of COVID-19 and monkeypox diseases with optimal control strategies and cost-benefit analysis, Franklin Open, 8, 100130.","DOI":"10.1016\/j.fraope.2024.100130"},{"key":"ref24","doi-asserted-by":"crossref","unstructured":"[24] Mondal, J., Samui, P., Chatterjee, A.N., and Ahmad, B. (2024), Modeling hepatocyte apoptosis in chronic HCV infection with impulsive drug control, Applied Mathematical Modelling, 136, 115625.","DOI":"10.1016\/j.apm.2024.07.032"},{"key":"ref25","doi-asserted-by":"crossref","unstructured":"[25] Sharma, S.K., Chatterjee, A.N., and Al Basir, F. (2023), Hopf bifurcation and optimal control of HCV\/HIV co-infection dynamics within humans: a theoretical study, Results in Control and Optimization, 11, 100234.","DOI":"10.1016\/j.rico.2023.100234"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"[26] Roy, P.K., Chatterjee, A.N., and Li, X.-Z. (2016), The effect of vaccination on dendritic cell and immune cell interaction in HIV disease progression, International Journal of Biomathematics, 9(1), 1650005.","DOI":"10.1142\/S1793524516500054"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"[27] Gumus, M. and Teklu, S.W. (2025), Cost-benefit and dynamical investigation of a fractional-order corruption population dynamical system, Fractal and Fractional, 9(4), 207.","DOI":"10.3390\/fractalfract9040207"},{"key":"ref28","doi-asserted-by":"crossref","unstructured":"[28] Gumus, M. and Turk, K. (2025), Global analysis of a monkeypox virus model considering government interventions, Physica Scripta, 100(045216).","DOI":"10.1088\/1402-4896\/ada318"},{"key":"ref29","doi-asserted-by":"crossref","unstructured":"[29] Bhunu, C.P. and Mushayabasa, S. (2012), Modelling the transmission dynamics of HIV\/AIDS and hepatitis B co-infection, HIV & AIDS Review, 11(4), 118-124.","DOI":"10.1016\/j.hivar.2012.04.001"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"[30] Grant, R.M. and Glidden, D.V. (2016), HIV moments and pre-exposure prophylaxis, The Lancet, 387(10027), 1507-1508.","DOI":"10.1016\/S0140-6736(16)30125-8"},{"key":"ref31","doi-asserted-by":"crossref","unstructured":"[31] Cohen, M.S., Chen, Y.Q., McCauley, M., Gamble, T., Hosseinipour, M.C., Kumarasamy, N., and Swindells, S. (2011), Prevention of HIV-1 infection with early antiretroviral therapy, New England Journal of Medicine, 365(6), 493-505.","DOI":"10.1056\/NEJMoa1105243"},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"[32] Anderson, R.M. and May, R.M. (1991), Infectious Diseases of Humans: Dynamics and Control, Oxford University Press.","DOI":"10.1093\/oso\/9780198545996.001.0001"},{"key":"ref33","doi-asserted-by":"crossref","unstructured":"[33] Grant, R.M., Lama, J.R., Anderson, P.L., McMahan, V., Liu, A., Vargas, L., and Buchbinder, S.P. (2010), Preexposure prophylaxis for HIV prevention in heterosexual men and women, New England Journal of Medicine, 363(27), 2587-2599.","DOI":"10.1056\/NEJMoa1011205"},{"key":"ref34","unstructured":"[34] Heffernan, J., McCarthy, K., McGowan, I., McGowan, C., and O'Brien, P. (2019), Efficacy of post-exposure prophylaxis for prevention of HIV infection, AIDS, 33(2), 403-410."},{"key":"ref35","unstructured":"[35] Mugavero, M.J., Norton, W.A., and Saag, M.S. (2009), Inconsistent retention in HIV care is associated with increased mortality, Clinical Infectious Diseases, 49(5), 927-932."},{"key":"ref36","unstructured":"[36] Sanchez, T.H., Dyer, T.V., and McGowan, I. (2016), Treatment interruptions and viral load rebound among HIV-positive individuals in the United States, Journal of Acquired Immune Deficiency Syndromes, 73(3), 302-309."},{"key":"ref37","doi-asserted-by":"crossref","unstructured":"[37] Cohen, M.S., Chen, Y.Q., McCauley, M., Gamble, T., Hosseinipour, M.C., Kumarasamy, N., and Swindells, S. (2011), Prevention of HIV-1 infection with early antiretroviral therapy, New England Journal of Medicine, 365(6), 493-505.","DOI":"10.1056\/NEJMoa1105243"},{"key":"ref38","doi-asserted-by":"crossref","unstructured":"[38] Diekmann, O., Heesterbeek, J.A.P., and Metz, J.A.J. (1990), On the definition and the computation of the basic reproduction ratio R_0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28(4), 365-382.","DOI":"10.1007\/BF00178324"},{"key":"ref39","doi-asserted-by":"crossref","unstructured":"[39] van den Driessche, P. and Watmough, J. (2002), Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180(1-2), 29-48.","DOI":"10.1016\/S0025-5564(02)00108-6"},{"key":"ref40","unstructured":"[40] Rodger, A.J., Cambiano, V., Bruun, T., and PARTNER Study Group (2016), Risk of HIV transmission through condomless sex in gay couples with suppressive ART: the PARTNER study, The Lancet, 388(10051), 298-310."},{"key":"ref41","doi-asserted-by":"crossref","unstructured":"[41] Castillo-Chavez, C. and Song, B. (2004), Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1(2), 361-404.","DOI":"10.3934\/mbe.2004.1.361"},{"key":"ref42","unstructured":"[42] UNAIDS (2024), 2024 UNAIDS global AIDS update summary for South Africa. https:\/\/www.unaids.org\/sites\/default\/files\/media_asset\/2024-unaids-global-aids-update-summary_en.pdf."},{"key":"ref43","unstructured":"[43] LaSalle, J.P. (1966), An invariance principle in the theory of stability, Technical report."},{"key":"ref44","doi-asserted-by":"crossref","unstructured":"[44] Naik, P.A., Zu, J., and Owolabi, K.M. (2020), Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control, Chaos, Solitons & Fractals, 138, 109826.","DOI":"10.1016\/j.chaos.2020.109826"},{"key":"ref45","doi-asserted-by":"crossref","unstructured":"[45] Zhu, L., Zhou, X., Li, Y., and Zhu, Y. (2019), Stability and bifurcation analysis on a delayed epidemic model with information dependent vaccination, Physica Scripta, 94, 125202.","DOI":"10.1088\/1402-4896\/ab2f04"},{"key":"ref46","doi-asserted-by":"crossref","unstructured":"[46] Blower, S.M. and Dowlatabadi, H. (1994), Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, International Statistical Review, 2, 229-243.","DOI":"10.2307\/1403510"}],"container-title":["Journal of Applied Nonlinear Dynamics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:42:48Z","timestamp":1788802968000},"score":1,"resource":{"primary":{"URL":"https:\/\/lhscientificpublishing.com\/index.php\/jand\/article\/view\/2493"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,7]]},"references-count":46,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2027,3,1]]}},"URL":"https:\/\/doi.org\/10.5890\/jand.2027.03.011","relation":{},"ISSN":["2164-6457","2164-6473"],"issn-type":[{"value":"2164-6457","type":"print"},{"value":"2164-6473","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,7]]}}}