Published May 21, 2025
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Optimal Control Analysis of HIV/AIDS Model with PrEP Strategy and Behavioral Changes
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- 1. Nigerian Army University Biu, Biu, Borno State, Nigeria
Description
Combining Pre-Exposure Prophylaxis (PrEP) with behavioral strategies has become vital in curbing HIV/AIDS transmission, offering a pathway to reduce infections and allocate health resources more effectively. In this study, we developed a six-compartment mathematical model to analyze the spread and control of HIV/AIDS. Through rigorous analysis, we calculated the basic reproduction number (R₀) to assess transmission potential and evaluated the stability of the disease-free equilibrium state. To identify optimal strategies for reducing HIV/AIDS prevalence, we designed an optimal control framework using Pontryagin’s Minimum Principle. This approach allowed us to evaluate the effectiveness of prevention tactics such as public health education, condom use, screening, and treatment both individually and in combination. Our findings highlight that pairing community awareness campaigns with increased condom usage among adults, alongside proactive screening and treatment programs, significantly reduces new infections and overall prevalence. Numerical simulations further demonstrated how these measures lower infection rates, aligning with our theoretical predictions. These insights emphasize the importance of integrated, multi-pronged interventions to guide public health policies and resource distribution in the fight against HIV/AIDS.
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References
- [1] Canadian Foundation for AIDS Research (CANFAR). History of HIV/AIDS [Internet]. 2023. Available from: http://canfar.com. Accessed 2 Jul 2024. [2] World Health Organization (WHO). HIV and AIDS: Key facts [Internet]. 2023. Available from: https://www.who.int/newsroom/fact-sheets/detail/hiv-aids. Accessed 2 Jul 2024. [3] Udoo I. J. M., Kimbir R. A., Odekunle R. M. (2015). Existence and uniqueness of solution of an HIV/AIDS model considering counseling, vaccination, and antiretroviral therapy (ART). Mathematical Theory and Modeling.;5(11). [4] World Health Organization (WHO). WHO expands its recommendation on the use of oral PrEP for HIV prevention [Internet]. 2015. Available from: https://www.who.int/news-room/recommendation-on-the-use-of-oral-PrEP/detail/hivaids. Accessed 2 Jul 2024. [5] World Health Organization (WHO). Policy brief on oral pre-prophylaxis of HIV infection (PrEP) [Internet]. 2015. Available from: http://www.who.int/hiv/prep/policy-brief-prep-2015/en/ [6] Oladejo J. K, and Oluyo T. O. (2022). Effects of PrEP on the HIV/AIDS dynamics with of immigration of infectives. International Journal of Mathematical Analysis and Modeling. 5(2):264-283. [7] Chinwendu E. and Martin, (2015). A Mathematical Modelling to study the impact of Irresponsible Infective Immigrants and vertical Transmission on the Dynamics of HIV/AIDS. J. Math. Comp. Sci. vol. (1): 72-92. [8] Dabbo M. I. and Seidu B. (2013). Modelling the Combine Effect of careless Susceptible and infective immigrants on the dynamics of HIV/AIDS, Journal of public Health & epidemiology. Vol 3(1), 362-369 [9] Issa S. and Massawe S. (2011). Modelling the effect of screening on the spread of HIV infection in a population with variable flow of of infective immigrants. Scientific Research and Essays. Vol 20. 4397-4405. [10] Lekan A. E., Momoh A. A., Tahir A. and Modibbo U. M. (2015). "On the Stability of Endemic Equilibrium State of HIV/AIDS Model with Irresponsible Infective Immigrants". Pacific Journal of Science and Technology. 16(2):225-233. [11] Mastahun M. and Abdurahman X. (2017). Optimal Control of an HIV/AIDS epidemic model with infective immigration and behavioural change. App .math, vol 8, 87-105. http://www.scirp.org/journal/am [12] Shim Eunha (2004). An Epidemic Model with Immigration of Infectives and Vaccination. Published Master's Thesis, University of British Columbia, Vancouver, BC Canada. [13] Mohammed, I. D. and Baba S.. (2012). Modelling the Effect of Irresponsible Infective Immigrants on the Transmission Dynamics of HIV/AIDS. Advances in Applied Mathematical Biosciences. ISSN 2248-9983 Volume 3, Number 1, pp. 31-40 International Research Publication House http://www.irphouse.com. [14] Kim S. B., Yoon M., Ku N. S., Kim M. H., Song J. E., (2014). Mathematical modeling of HIV prevention measures including pre-exposure prophylaxis on HIV incidence in South Korea. PLoS ONE 9, no. 3, e90080, 1–9. http://doi.org/10.1371/journal.pone.0090080 [15] Abbas U. L., Anderson R. M., Mellors J. W. (2007). Potential impact of antiretroviral chemoprophylaxis on HIV-1 transmission in resource-limited settings. PloS one. 2007 Sep 19;2(9):e875. [16] Silva C. J. and Torres, D. F. M. (2017). Modeling and Optimal Control of HIV/AIDS Prevention through PrEP. Ar Xiv:1703.06446v2 [math.oc] http://dx.doi.org/10.3934/dcdss.2018008. [17] Afassinou K., Chirove F., Govinder K. S. (2017). Pre-exposure prophylaxis and antiretroviral treatment interventions with drug resistance. Mathematical-Bioscience. 285:92-101. Doi;10.1016/j.mbs,2017.01.005 [18] Drabo E. F., Hay J. W., Vardavas R., Wagner Z. R., Sood N ., (2016). A cost-effectiveness analysis of pre-exposure prophylaxis for the prevention of HIV among Los Angeles County men who have sex with men. Clinical Infectious Diseases. 1;63(11):1495-504. doi:10.1093/cid/ciw578. [19] Moya E. M., Rodrigues D. S., Pietrus A., Severo A. M. (2022). A mathematical model for HIV/AIDS under preexposure and post-exposure prophylaxis. Biomath.2022;11(2):2208319 [20] Mastahun, M. and Abdurahman, X. (2017). Optimal Control of an HIV/AIDS epidemic model with infective immigration and behavioural change. App.math, vol 8, 87-105. http://www.scirp.org/journal/am [21] Musa R., Robert W., and Nabendra P., (2012). Optimal control and sensitivity Analysis of an HIV/AIDS-Resistant Model with Behavioral Change. Springer Nature. 69(4) 543- 589. doi;10.1007/s10441-021-09421-3 [22] Valesco and Hsieh, Y. H. (1994). Modelling the effect of Treatment and behaviour in the dynamics of HIV change in behavior and sexual industry: Its implications for spread of HIV/AIDS, Bull. Math. Biol. 66 143 166 [23] Akudibillah, Gordon & Pandey, Abhishek & Medlock, (2019). Optimal control for HIV treatment. Mathematical Biosciences and Engineering. 16. 373-396. Doi:10.3934/mbe.2019018 [24] Ayele T. K., Goufo E. F. D., Mugisha S, (2021) Mathematical modeling of HIV/AIDS with optimal control: A case study in Ethiopia, Results in Physics, Volume 26, 104263, ISSN 2211-3797. https://doi.org/10.1016/j.rinp.2021.104263 [25] Odebiyi O. A., Oladejo J. K., Elijah E. O., Olajide O. A., Taiwo A. A., Taiwo A. J. (2024). Mathematical modeling on assessing the impact of screening on HIV/AIDS transmission dynamics. Journal of Applied Sciences and Environmental Management. 2024;28(8):2347-2357. [26] World Health Organization (WHO). World Health Organization Data [Internet] 2025. Available from: https://www.who.int/data/gho/data/countries/country-details/GHO/nigeria?hl=en-GB. Accessed 27/5/2025 [27] L.S. Pontragin, R.V. Gamkrelize, V.G. Boltyanskii, and E.F. Mishchenko, (1962). The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.