Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach

Authors

  • Saheed Ajao Department of Mathematics and Computer Science, Elizade University, Ilara-mokin, Ondo State. Nigeria
  • Isaac Olopade Department of Mathematics and Statistics, Federal University Wukari, Wukari. Taraba State. Nigeria
  • Titilayo Akinwumi Department of Mathematics and Computer Science, Elizade University, Ilara-mokin, Ondo State. Nigeria
  • Sunday Adewale Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso. Oyo State. Nigeria
  • Adelani Adesanya Department of Mathematics and Computer Science, Elizade University, Ilara-mokin, Ondo State. Nigeria

Keywords:

HIV/AIDS, Global stability, Bifurcation, Lyapunov function

Abstract

New challenges like the outbreak of new diseases, government policies, war and insurgency etc. present distortion, delay and denial of persons’ access to ART, thereby fuelling the spread and increasing the burden of HIV/AIDS. A mathematical model is presented to study the transmission dynamics and control of HIV infection. The qualitative and quantitative analyses of the model are carried out. It is shown that the disease-free equilibrium of the model is globally asymptotically stable whenever the basic reproduction number is less than unity. It is also shown that a unique endemic equilibrium exists whenever the basic reproduction number exceeds unity and that the model exhibits a forward bifurcation. Furthermore, the Lyapunov function is used to show that the endemic equilibrium is globally asymptotically stable for a special case of the model whenever the associated basic reproduction number is greater than unity. The model is calibrated to the data on HIV/AIDS prevalence in Nigeria from 1990 to 2019 and it represents reality. The numerical simulations on the global stability of disease-free equilibrium and endemic equilibrium justify the analytic results. The fraction of the detected individuals who stays in the treatment class plays a significant role as it influences the population of the latently-infected individuals and AIDS class by preventing individuals from progressing into the AIDS class.

Dimensions

D. T. Hamilton, D. A. Katz, W. Luo, J. D. Stekler, E. S. Rosenberg, P. S. Sullivan, S. M. Goodreau, & S. Cassels, “Effective strategies to promote HIV self-testing for men who have sex with men: Evidence from a mathematical model”, Epidemics 37 (2021) 100518. https://doi.org/10.1016/j.epidem.2021.100518

K. Giguere, J. W. Eaton, K. Marsh, L. F. Johnson, C. C. Johnson, E. Ehui,` A. Jahn, I. Wanyeki, F. Mbofana, F. Bakiono, M. Mahy, & M. MaheuGiroux, “Trends in knowledge of HIV status and efficiency of HIV testing services in sub-Saharan Africa, 2000–20: a modelling study using survey and HIV testing programme data”, The Lancet HIV 8 (2021) 284. https://doi.org/10.1016/S2352-3018(20)30315-5.

World Health Organization: HIV: Key Facts. Available at https://www. who.int/news-room/fact-sheets/detail/hiv-aids. Accessed on 03/01/2023

M. Schwikowski, “Why do African children lack HIV treatment?” Available at https://www.dw.com/en/africa-un-reports-dire-l ack-in-childrens-hiv-treatment/a-58769989. Accessed on 16/12/2022

UNAIDS: Children: Indonesia: “Helping one family at a time through Lentera Anak Pelangi’s One Child One life program”. Available at ht tps://www.unaids.org/en/keywords/children. Accessed on

/12/2022.

Human Rights Watch, “Deadly Denial: Barriers to HIV/AIDS treatment for people who use drugs in Thailand”. Available at https://www.hr w.org/report/2007/11/28/deadly-denial/barriers-hiv/a ids-treatment-people-who-use-drugs-thailand. Accessed on 16/12/2022

B. Cooper, Hunger as a barrier for HIV treatment, The Lancet Infectious Diseases 22(3) (2022) 328. https://doi.org/10.1016/S1473-3099(22)00072-X

N. Crooks, R. B. Singer, A. Smith, E. Ott, G. Donenberg, A. K. Matthews, C. L. Patil, S. Haider & A. K. Johnson, “Barriers to PrEP uptake among Black female adolescents and emerging adults”, Preventive Medicine Reports 31 (2023) 102062. doi:10.1016/j.pmedr.2022.102062.

S. C. Kalichman, S. Catz & B. Ramachandran, “Barriers to HIV/AIDS treatment and treatment adherence among African-American adults with disadvantaged education” J Natl Med Assoc 91 (1999) 439.

Rural Health Information Hub, “Barriers to HIV/AIDS Care in Rural Communities”. Available at https://www.ruralhealthinfo.org/ toolkits/hiv-aids/1/rural-barriers. Accessed on 20/01/2023.

T. G. Heckman, A. M. Somlai, J. Peters, J. Walker, L. Otto-Salaj, C. A. Galdabini & J. A. Kelly, “Barriers to care among persons living with HIV/AIDS in urban and rural areas” AIDS Care, 10(3) (1998) 365. doi:10.1080/713612410.

M. Kretzschmar, “Disease modeling for public health: added value, challenges and institutional constraints”. J Public Health Policy 41 (2020) 39.

D. Dimitrov, D. Wood, A. Ulrich, D. A. Swan, B. Adamson, J. R. Lama, J. Sanchez & A. Duerr, “Projected effectiveness of HIV detection during early infection and rapid ART initiation among MSM and transgender women in Peru: A modeling study”, Infectious Disease Modelling 4 (2019) 73. https://doi.org/10.1016/j.idm.2019.04.001

P. Ngina, R. W. Mbogo, & L. S. Luboobi, “HIV drug resistance: Insights from mathematical modelling”, Applied Mathematical Modelling 75 (2019) 141. https://doi.org/10.1016/j.apm.2019.04.040

L. Cai, X. Li, M. Ghosh, B. Guo, “Stability analysis of an HIV/AIDS epidemic model with treatment”, Journal of Computational and Applied Mathematics 229 (2009) 313. https://doi.org/10.1016/j. cam.2008.10.067

A. S. Hassan & N. Hussaini, “Analysis of an HIV - HCV simultaneous infection model with time delay”, J. Nig. Soc. Phys. Sci. 3 (2021) 1. ht tps://doi.org/10.46481/jnsps.2021.109

O. O. Apenteng, P. P. Osei, B. Oduro, M. P. Kwabla & N. A. Ismail, “The impact of implementing HIV prevention policies therapy and control strategy among HIV and AIDS incidence cases in Malaysia”, Infectious Disease Modelling 5 (2020) 755. https://doi.org/10.1016/ j.idm.2020.09.009

W. Yang, Z. Shu, J. Lam & C. Sun, “Global dynamics of an HIV model incorporating senior male clients”, Applied Mathematics and Computation 311 (2017) 203. https://doi.org/10.1016/j.amc.2017.05.030

P. Dubey, U. S. Dubey & B. Dubey, “Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection”, Mathematics and Computers in Simulation 144 (2018) 120. https://doi.org/10.1016/j.matcom.2017.07.006.

I. Ghosh, P. K. Tiwari, S. Samanta, I. M. Elmojtaba, N. Al-Salti & J. Chattopadhyay, “A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear”, Mathematical Biosciences, 306 (2018) 160. https://doi.org/10.1016/j.mbs.2018.09.014

The World Bank: Fertility rate ,total(birth rate per woman). Available at https://data.worldbank.org/indicator/SP.DYN.TFRT.IN?e nd=1990&start=1960. Accessed on 20/12/2022.

The World Bank: Data: Life expectancy at birth,total(years)-Nigeria.

Available at https://data.worldbank.org/indicator/SP.DY N.LE00.IN?end=2019&locations=NG&start=1960. Accessed on 20/12/2022.

R. Aggarwal, “Dynamics of HIV-TB co-infection with detection as optimal intervention strategy”, International Journal of Non-Linear Mechanics 120 (2020) 103388. https://doi.org/10.1016/j.ijnonlinme c.2019.103388.

World Health Organization, “HIV/AIDS-protection and early detection, promise of health”. Available at https://www.afro.who.int/news/ hivaid-protection-and-early-detection-promise-health. Accessed on 20/12/2022

P. van den Driessche & J. Watmough, “Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission”, Mathematical Biosciences 180 (2002) 29.

S. A. Ayuba, I. Akeyede & A. S.Olagunju, “Stability and Sensitivity Analysis of Dengue-Malaria Co-infection Model in Endemic Stage” Journal of the Nigerian Society of Physical Sciences 3(2021) 96.

J.P. LaSalle, The stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, (1976).

J. Carr, Applications of Centre Manifold Theory Applied Mathematical Sciences. Springer-Verlag, New York, 35 (1982).

C. Castillo-Chavez & B. Song, “Dynamical models of tuberculosis and their applications”, Math Biosci Eng 1 (2004) 361.

Our World in Data: Prevalence, new cases and deaths from HIV/AIDS, Nigeria,1990 to 2019. Available at https://ourworldindata.org/grapher/deaths-and-new-cases-of-hiv?country=~NGA. Accessed on 16/12/2022

Our World in Data: Population, 10000 BCE to 2021. Available at https://ourworldindata.org/grapher/population?country=~NGA. Accessed on 16/12/2022

Published

2023-04-19

How to Cite

Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1389. https://doi.org/10.46481/jnsps.2023.1389

Issue

Volume 5, Issue 2, May 2023

Section

Original Research
Copyright & Licensing

Copyright (c) 2023 Saheed Ajao, Isaac Olopade, Titilayo Akinwumi, Sunday Adewale, Adelani Adesanya

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach. (2023). Journal of the Nigerian Society of Physical Sciences, 5(2), 1389. https://doi.org/10.46481/jnsps.2023.1389