Mathematical dynamics for HIV infections with public awareness and viral load detectability

Year 2023, Volume: 3 Issue: 3, 256 - 280, 30.09.2023

Umar Tasiu Mustapha , Abdurrahman Ado , Abdullahi Yusuf , Sania Qureshi , Salihu Sabiu Musa

https://doi.org/10.53391/mmnsa.1349472

Cited By: 3

Abstract

In this paper, we develop a nonlinear deterministic model that incorporates public awareness and treatment to describe the dynamics of HIV/AIDS in an infected population with detectable and undetectable viral load. The model undergoes backward bifurcation in which a stable disease-free equilibrium coexists with a stable endemic equilibrium. Numerical simulations carried out show the behavior of the state variables and the impact of public awareness in controlling the spread of HIV. The results show that public awareness will help in curtailing the spread of HIV infection, and when treatment is applied to infected individuals with detectable viral load can easily suppress their virus to become undetectable so that they cannot transmit HIV through sexual intercourse.

Keywords

HIV, viral load detectability, parameter calibration, bifurcation analysis, confidence interval

References

• Swain, S.L., McKinstry, K.K. and Strutt, T.M. Expanding roles for CD4+ T cells in immunity to viruses. Nature Reviews Immunology, 12, 136-148, (2012).
• Wilson, D.P., Law, M.G., Grulich, A.E., Cooper, D.A. and Kaldor, J.M. Relation between HIV viral load and infectiousness: a model-based analysis. The Lancet, 372(9635), 314-320, (2008).
• Center for Disease Control and Prevention. About HIV https://www.cdc.gov/hiv/basics/whatishiv.html, (2021).
• World Health Organization. HIV and AIDS www.who.int/news-room/fact-sheets/detail/hiv-aids, (2021).
• HIV.gov. The Global HIV and AIDS Epidemic https://www.hiv.gov/hiv-basics/overview/data-andtrends/global-statistics, (2021).
• Podder, C.N., Sharomi, O., Gumel, A.B. and Strawbridge, E. Mathematical analysis of a model for assessing the impact of antiretroviral therapy, voluntary testing and condom use in curtailing the spread of HIV. Differential Equations and Dynamical Systems, 19, 283-302, (2011).
• Gaardbo, J.C., Hartling, H.J., Gerstoft, J. and Nielsen, S.D. Thirty years with HIV infection—nonprogression is still puzzling: lessons to be learned from controllers and long-term nonprogressors. AIDS Research and Treatment, 2012, (2012).
• Mandalia, S., Westrop, S.J., Beck, E.J., Nelson, M., Gazzard, B.G. and Imami, N. Are long-term non-progressors very slow progressors? Insights from the Chelsea and Westminster HIV cohort, 1988–2010. PLoS One, 7(2), e29844, (2012).
• Nam aids map HIV & AIDS-sharing knowledge, changing lives. Viral load https://www.aidsmap.com/about-hiv/viral-load, (2017).
• Hussaini, N., Winter, M. and Gumel, A.B. Qualitative assessment of the role of public health education program on HIV transmission dynamics. Mathematical Medicine and Biology: A Journal of the IMA, 28(3), 245-270, (2011).
• Waziri, A.S., Massawe, E.S. and Makinde, O.D. Mathematical modelling of HIV/AIDS dynamics with treatment and vertical transmission. Applied Mathematics, 2(3), 77-89, (2012).
• Bhunu, C.P., Mushayabasa, S., Kojouharov, H. and Tchuenche, J.M. Mathematical analysis of an HIV/AIDS model: impact of educational programs and abstinence in sub-Saharan Africa. Journal of Mathematical Modelling and Algorithms, 10, 31-55, (2011).
• Silva, C.J. and Torres, D.F. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecological Complexity, 30, 70-75, (2017).
• Naik, P.A., Owolabi, K.M., Yavuz, M. and Zu, J. Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells. Chaos, Solitons & Fractals, 140, 110272, (2020).
• Naik, P.A., Zu, J. and Owolabi, K.M. Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order. Physica A: Statistical Mechanics and its Applications, 545, 123816, (2020).
• Naik, P.A., Yavuz, M. and Zu, J. The role of prostitution on HIV transmission with memory: A modeling approach. Alexandria Engineering Journal, 59(4), 2513-2531, (2020).
• Naik, P.A., Zu, J. and Owolabi, K.M. Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control. Chaos, Solitons & Fractals, 138, 109826, (2020).
• Ahmed, I., Akgül, A., Jarad, F., Kumam, P. and Nonlaopon, K. A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis. Mathematical Modelling and Numerical Simulation with Applications, 3(2), 170-187, (2023).
• Ghosh, D., Santra, P.K. and Mahapatra, G.S. A three-component prey-predator system with interval number. Mathematical Modelling and Numerical Simulation with Applications, 3(1), 1-16, (2023).
• Sabbar, Y. Asymptotic extinction and persistence of a perturbed epidemic model with different intervention measures and standard lévy jumps. Bulletin of Biomathematics, 1(1), 58-77, (2023).
• Joshi, H., Yavuz, M. and Stamova, I. Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law. Bulletin of Biomathematics, 1(1), 24-39, (2023).
• Moore, G. AM Stuart and AR Humphries Dynamical systems and numerical analysis (Cambridge Monographs on Applied and Computational Mathematics No. 2, Cambridge University Press, 1996). Proceedings of the Edinburgh Mathematical Society, 41(1), 213-216, (1998).
• Smith, H.L. Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems: an introduction to the theory of competitive and cooperative systems (Vol. 41). American Mathematical Society, (1995).
• Van den Driessche P. and Wanmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180, 29-48, (2000).
• Castillo-Charvez, C. and Song, B. Dynamical model of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2), 361-404, (2004).
• Lasalle, J.P. The stability of dynamical systems. Regional conference series in applied mathematics, SIAM, Philadelphia, (1976).
• Berg, M.G., Olivo, A., Harris, B.J., Rodgers, M.A., James, L., Mampunza, S. et al. A high prevalence of potential HIV elite controllers identified over 30 years in Democratic Republic of Congo. eBioMedicine, 65, 103258, (2021).
• Yusuf, A., Mustapha, U.T., Sulaiman, T.A., Hincal, E. and Bayram, M. Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative. Chaos, Solitons & Fractals, 145, 110794, (2021).
• Mustapha, U.T. and Hincal, E. An optimal control of hookworm transmissions model with differential infectivity. Physica A: Statistical Mechanics and its Applications, 545, 123625, (2020).