## Mathematical Modelling and Analyzing the Dynamics of Condom Efficacy and Compliance in the Spread of HIV/AIDS

Published: 2024-02-03

Page: 54-65

Department of Mathematics and Statistics, Federal University Wukari, PMB 1020, Taraba State, Nigeria.

Sangoniyi Sunday Oloruntoyin

Department of Mathematics and Computing Science Education, Emmanuel Alayande University of Education, Oyo, Oyo State, Nigeria.

Philemon Musa Emmanuel

Department of Mathematics and Statistics, Federal University Wukari, PMB 1020, Taraba State, Nigeria.

Department of Mathematics and Social Sciences, Osun State Polytechnic Iree, Nigeria.

Department of Physical Sciences, Chrisland University, P.M.B. 2131, Abeokuta, Ogun State,Nigeria.

Department of Mathematics and Computer Science, Elizade University, Ondo State, Nigeria.

Aishah Umar Mamman

Department of Mathematics and Statistics, Federal University Wukari, PMB 1020, Taraba State, Nigeria.

Department of Mathematics and Statistics, Federal University Wukari, PMB 1020, Taraba State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

The study involves a mathematical analysis of condom efficacy and compliance in the transmission of HIV/AIDS. It explores how condom use impacts the prevention of HIV/AIDS and considers other epidemiological factors affecting the progression from HIV to full-blown AIDS. The model's existence and uniqueness of solution are established, with a focus on the basic reproduction number, representing the average new infections caused by an infected individual. The analysis reveals that the disease-free equilibrium is stable when the basic reproduction number is below unity i.e., but becomes endemic otherwise, i.e.. Sensitivity analysis indicates parameters with positive values increase the reproduction number, emphasizing that the effective contact rate should not exceed 0.22 to avoid the endemic stage. Numerical simulations using MAPLE 18 software demonstrate that condom compliance reduces the dynamic spread of HIV, and targeted immunity boost controls the viral load.

Keywords: HIV/AIDS, treatment, condom efficiency, condom compliance, basic reproduction number and equilibrium points

#### How to Cite

Adesola, O. I., Oloruntoyin, S. S., Emmanuel , P. M., Temilade , M. I., Adeyemi , A. G., Oladele , A. S., Mamman , A. U., & Kareem , A. A. (2024). Mathematical Modelling and Analyzing the Dynamics of Condom Efficacy and Compliance in the Spread of HIV/AIDS. Asian Research Journal of Current Science, 6(1), 54–65. Retrieved from https://globalpresshub.com/index.php/ARJOCS/article/view/1944

### References

Global HIV & AIDS statistics -fact sheet; 2020.

Huo HF, Chen R, Wang XY. Modelling and stability of HIV/AIDS epidemic model with treatment. Appl. Math. Model. 2016;40:6550-6559.

Ibrahim IA, Daniel EE, Danhausa AA, Adamu MU, Shawalu CJ, Yusuf A. Mathematical modeling of dynamics of HIV transmission depicting the ımportance of counseling and treatment. J. Appl. Sci. Environ. Management. 2021;25(6): 893-903.

World Health Organization (WHO), HIV & AIDS — fact sheet; 2023.

Centers for disease control and prevention: Condom distribution as a structural intervention. Division of HIV/AIDS Prevention, Atlanta, GA. Available:https://www.cdc.gov/hiv/pdf/programresources/guidance/condoms/cdc-hiv-condom-distribution.pdf Fractals

Gelaw YA, Williams G, Soares RJ, Gilks CF, Assefa Y. HIV prevalence among tuberculosis patients in Sub-Saharan Africa: A systematic review and meta-analysis. AIDS Behav. 2019;23(6):1561–75.

Global progress report on HIV, viral hepatitis and sexually transmitted infections; 2021.

Owolabi, Atangana A. Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative; 2019.

Udoy SB, et al. Mathematical study of HIV and HSV-2 Co-infection. American Journal of Mathematics and Statistics. 2015;5(1):15-23.

Seeley J, Nakiyingi-Miiro A Kamali, Mpendo J, Asiki G, Abaasa A. High HIV incidence and socio-behavioral risk patterns in fishing communities on the shores of Lake Victoria,Uganda. Sexually Transmitted Diseases. 2012;39(6):433-9.

Endalamaw S Ambachew, Geremew D, Habtewold T. HIV infection and unknown HIV status among tuberculosis patients in Ethiopia: A systematic review and meta-analysis. Int J Tuberculosis Lung Disease. 2019;23(2):187–94.

Ghosh Tiwari P, Samanta S, Elmojtaba I, Al-Salti N, Chattopadhyay J. A simple si-type model for HIV/AIDS with media and self-imposed psychological fear. Math Biosci. 2018;306:160-169.

Toro HD, Trujillo CA, Carranza EM. Mathematical model Describing HIV infection with Time- Delayed CD4T,- cell Activation. Processes. 2020;8(7):782. Available:https: //doi.org/10.3390/pr 8070782

Ajao SO, Olopade IA, Akinwumi T, Adewale SO, Adesanya AO. Understanding the transmission dynamics and control of HIV ınfection: A mathematical model approach. Journal of the Nigerian Society of Physical Sciences. 2023;5(2):1389.

Adewale SO, Olopade IA, Ajao SO, Mohammed IT. Mathematical analysis of sensitive parameters on the dynamical spread of HIV. International Journal of Innovative Research in Science, Engineering and Technology. 2016;5(5):2624-2635.

Akinwumi TO, Olopade IA, Adesanya AO, Alabi MO. A mathematical model for the transmission of HIV/AIDS with early treatment. Journal of Advances in Mathematics and Computer Science. 2021;36(5):35-51.

Adewale SO, Olopade IA, Ajao SO, Adeniran GA. Mathematical analysis of diarrhea in the presence of vaccine. International Journal of Scientific and Engineering Research. 2015;6(12):396-404.

Anderson RM. The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS. J. AIDS. 2001;1:214-256.

Bushnaq S, Shah K, Zaman G. Existence theory of HIV- 1 infection model by using arbitrary order derivative of without singular kernel type. Journal of Mathematical Analysis. 2018;9(1):16-28.

Hamou E Azroul, Bouda S, Guedd M. Mathematical modelling of HIV transmission in a heterosexual population: incorporating memory conservation. Available:https://www.researchgate.net/publication / 371179334, 2023

Hussaini N, Gumel M. Qualitative assesment of the role of public health education program on HIV transmission dynamics, Mathematical Medicine and Biology. 2011;245–270.

Marsudi M, Andari A. Sensitivity analysis of effect of screening and HIV therapy on the dynamics of spread of HIV, Applied Mathematical Sciences. 2014;8(155):7749–7763.

Marsudi M, Hidayat N, Wibowo R. A sensitivity analysis of the ımpact of educational campaign, Screening and therapy on the spread of HIV ınfection. Nonlinear Analysis and Differential Equations. 2016;4(7):32–341.

Mukandavire Z, Garira W, Tchuenche J. Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics, Applied Mathematical Modelling. 2009;33(4):2084–2095.

Olopade IA, Adewale SO, Mohammed IT, Ajao SO, Oyedemi OT. Mathematical analysis of the role of detection in the dynamical spread of HIV-TB Co-infection. Journal of Advances in Mathematics. 2016;11(10):5715-5740.

Safiel R, Massawe ES, Makinde DO. Modelling the effect screening and treatment on transmission of HIV/AIDS ınfection in a population, American Journal of Mathematics and Statistics. 2012;75-88.

Sanna MS. Memory and media coverage effects on an HIV/AIDS epidemic mode with treatment. Journal of Computational and Applied Mathematics. 2021;385.

Adewale SO, Olopade IA, Adeniran GA, Mohammed IT, Ajao SO. Mathematical analysis of effects of ısolation on ebola transmission dynamics. Researchjournali’s Journal of Mathematics. 2015;2(2):1-20.

Musibau O, Muritala AA, Isaac AO, Adelani OA, Akeem OY. Mathematical analysis of sensitive parameters due to dynamic transmission of Ebola virus disease.Comprehensive Research and Reviews in Multidisciplinary Studies. 2022;01(01):001–016.

Olopade A, Adesanya AO, Mohammed IT. Mathematical analysis of the global dynamics of an SVEIR epidemic model with herd ımmunity. International Journal of Science and Engineering Investigations. (IJSEI). 2017;6(69):141-148.

Olopade A, Adesanya AO,Akinwumi TO. Mathematical transmission of SEIR epidemic model with natural ımmunity. Asian Journal of Pure and Applied Mathematics. 2021;3(1):19-29.

Olopade IA, Adewale SO, Mohammed IT, Adeniran GA, Ajao SO, Ogunsola AW. Effect of effective contact tracing in curtaining the spread of Covid-19. Asian Journal of Research in Biosciences.2021;3(2):118-134.

Olopade IA, Ajao SO, Adeniran GA, Adamu AK, Adewale SO, Aderele OR. Mathematical transmission of tuberculosis (TB) with Detection of Infected Undetectected. Asian Journal of Research in Medicine and Medical Sciences. 2022;4(1):100-119.