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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Modelling of HIV Pathogens' Impact on the AIDS Disease Transmission with Optimal Control Analysis

Journal of Applied Nonlinear Dynamics 13(3) (2024) 571--582 | DOI:10.5890/JAND.2024.09.012

Abdisa Shiferaw Melese$^{1}$, Legesse Lemecha Obsu$^{1}$, Eshetu Dadi Gurmu$^{2}$

$^{1}$ Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia

$^{2}$ Department of Mathematics, Samara University, Afar, Ethiopia

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Abstract

HIV is a viral pathogen that weakens a human's immune organ, making it vulnerable to infectious diseases. This study focuses on a nonlinear deterministic mathematical model for the impact of HIV pathogens on AIDS disease transmission with optimal control analysis. Equilibrium points and basic reproduction number are computed. The qualitative analysis of the model revealed the scenario for both HIV-free and endemic equilibrium points. The local stability of the equilibrium is established via the Routh-Hurwitz criteria, while the global stability of the equilibrium is justified by using a Lyapunov function. Also, the normalized sensitivity analysis is performed. We extended the proposed model into an optimal control problem by incorporating four control variables, namely, a safer sex programme, a preventive measure, a condom usage programme, and medical care. Furthermore the optimal control is found by minimizing the number of HIV/AIDS individuals. Finally, the numerical simulations show agreement with the analytical results.

References

  1. [1]  World Health Organization. (2007), Guide to starting and managing needle and syringe programmes, USA: Geneva.
  2. [2]  World Health Organization. (2019), Global status report on alcohol and health 2018, World Health Organization.
  3. [3] Alyobi, S. and Yassen, M.F. (2022), A study on the transmission and dynamical behavior of an HIV/AIDS epidemic model with a cure rate, AIMS Mathematics, 7(9), 17507-17528.
  4. [4]  Ngina, P., Mbogo, R.W., and Luboobi, L.S. (2018), Modelling optimal control of in-host HIV dynamics using different control strategies, Computational and Mathematical Methods in Medicine, 18.
  5. [5] Oyovwevotu, S.O. (2021), Mathematical modelling for assessing the impact of intervention strategies on HIV/AIDS high risk group population dynamics, Heliyon, 7, e07991.
  6. [6]  Rabiu, M., Willie, R., and Parumasur, N. (2021), Optimal control strategies and sensitivity analysis of an Hiv/Aids-resistant model with behavior change, Acta Biotheoretica, 69, 543--589.
  7. [7]  Blankson, J. (2010), Control of HIV-1 replication in elite suppressors, Discovery Medicine, 9(46),261--266.
  8. [8]  Alsahafi, S. and Woodcock, S. (2022), Exploring HIV dynamics and an optimal control strategy, Mathematics, 10(5), 749.
  9. [9]  Elaiw, A.M., Alshehaiween, S.F., and Hobiny, A.D. (2020), Global properties of HIV dynamics models including impairment of B-cell functions, Journal of Biological Systems, 28(01), 1-25.
  10. [10]  Reynell, L. and Trkola, A. (2012), HIV vaccines: an attainable goal?, Swiss Medical Weekly, 142: w13535.
  11. [11]  Kapadiya, M.N. (2022), Aids case study, International Journal of Nursing Education and Research, 10(1), 21-22.
  12. [12]  WHO. (2007), WHO case definitions of HIV for surveillance and revised clinical staging and immunological classification of HIV-related disease in adults and children, Switzerlan: Geneva.
  13. [13]  Oukouomi Noutchie, S.C., Kitio Kwuimy, C.A., Tewa, J.J., Nyabadza, F., and Bildik, N. (2015), Computational and theoretical analysis of human diseases associated with infectious pathogens, Research International, 2015.
  14. [14]  Van den Driessche, P. and Watmough, J. (2002), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180(1-2), 29-48.
  15. [15]  Mojeeb, A., Osman, E., and Isaac, A.K. (2017), Simple mathematical model for malaria transmission, Journal of Advances in Mathematics and Computer Science, 25(6), 1-24.
  16. [16]  LaSalle, J.P. (1976), The stability of dynamical systems, regional conference series in applied Mathematics, SIAM: Philadelphia.
  17. [17] Fleming, W.H. and Rishel, R.W. (2012), Deterministic and stochastic optimal control, Heidelberg Berlin: New York.
  18. [18] Lukes, D. (1982), Differential equations: Classical to controlled, USA: DA.
  19. [19] Lenhart, S. and Workman, J.T. (2007), Optimal control applied to biological models, CRC press: New York.
  20. [20]  Ram, N., Agraj, T., and Dileep, S. (2011), A nonlinear HIV/AIDS model with contact tracing, Applied Mathematical Modelling, 217, 9575-9591.
  21. [21]  Ayele, T.K., 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.
  22. [22]  Melese, A.S. (2022), Modelling of pathogens impact on the human disease transmission with optimal control strategies, Journal of Mathematical Sciences, 1-21.
  23. [23]  Bakare, E.A. and Nwozo, C.R. (2017), Bifurcation and sensitivity analysis of malaria-schistosomiasis co-infection model, International Journal of Applied and Computational Mathematics, 3, 971-1000.
  24. [24]  Liu, D. and Wang, B. (2013), A novel time delayed HIV/AIDS model with vaccination and antiretroviral therapy and its stability analysis, Applied Mathematical Modelling, 37(7), 4608-4625.
  25. [25]  Wattanasirikosone, R. and Modnak, C. (2022), Analysing transmission dynamics of HIV/AIDS with optimal control strategy and its controlled state, Journal of Biological Dynamics, 16(1), 499-527.
  26. [26]  Naresh, R. and Sharma, D. (2011), An HIV/AIDS model with vertical transmission and time delay, World Journal of Modelling and Simulation, 7(3), 230-240.
  27. [27] Boltyanskiy, V.G., Gamkrelidze, R.V., Mishchenko, Y., and Pontryagin, L.S. (1962), Mathematical Theory of Optimal Processes, John Wiley and Sons, London: UK.
  28. [28]  Alimonti, J.B., Ball, T.B., and Fowke, K.R. (2003), Mechanisms of CD4$^+$ T lymphocyte cell death in human immunodeficiency virus infection and AIDS, The Journal of General Virology, 84(7), 1649-1661.
  29. [29]  Hel, Z., McGhee, J.R., and Mestecky, J. (2006), HIV infection: first battle decides the war, Trends in Immunology, 27(6), 274-81.
  30. [30]  Crosby, R. and Bounse, S. (2012), Condom effectiveness: where are we now?, Sexual Health, 9 (1), 10-17.
  31. [31]  Coutsoudis, A., Kwaan, L., and Thomson, M. (2010), Prevention of vertical transmission of HIV-1 in resource-limited settings, Expert Review of Anti-Infective Therapy, 8(10), 1163-75.
  32. [32]  Holt, M., Lea, T., Mao, L., Kolstee, J., Zablotska, I., and Dick, T. (2018), Community-level changes in condom use and uptake of HIV pre-exposure prophylaxis by gay and bisexual men in Melbourne and Sydney, Australia: results of repeated behavioural surveillance in 2013--17, The Lancet HIV, 5(8), e448-e456.
  33. [33]  Antiretroviral Therapy Cohort Collaboration. (2008), Life expectancy of individuals on combination antiretroviral therapy in high-income countries: a collaborative analysis of 14 cohort studies, The Lancet, 372(9635), 293-99.
  34. [34]  May, M.T. and Ingle, S.M. (2011), Life expectancy of HIV-positive adults: a review, Sexual Health, 8(4), 526-33.

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