Issue

Vol. 9 No. 2 (2020): SPECIAL ISSUE OF SCIENCE, 2020

Date Log

Submitted
Nov 18, 2020
Published
Nov 19, 2020

Modelling Optimal Control of Heavy Alcohol Consumption on the Transmission Dynamics of HIV/AIDS

https://doi.org/10.56279/jhss.v9i2.49
G. Mwanga
Ongodia
Kampala, Uganda

Journal of Humanities & Social Science (JHSS), Vol. 9 No. 2 (2020): SPECIAL ISSUE OF SCIENCE, 2020

Abstract

Unhealthy consumption of alcohol continues to be found everywhere in our
communities leading to behavioural and physiological effects on neuro-cognitive
function. This results into high-risk sexual behaviour mainly due to impaired decisionmaking capacity and impulsivity, a catalyst of HIV infection and ultimately AIDS. This
paper investigates the best control combination for HIV/AIDS pandemic in a
community with alcohol abuse problem. It proposes a compartmental deterministic
model for the transmission dynamics of HIV/AIDS in a community plagued with
alcohol abuse. The paper determines the implementation of optimal control
strategies involving reduction of new HIV cases through the ABC (abstinence, being
faithful, and use of condoms) campaign, treatment of alcohol abusers and prevention
of alcohol relapse using Pontryagin's maximum principle. Numerical simulations are
implemented using the forward-backward sweep method, and the pertinent results
are presented graphically and discussed quantitatively. Based on performance, results
from numerical simulations depict that the best results are obtained when the three
strategies are used simultaneously.
Keywords: ; ; optimal control; ABC strategy; .

Keywords

HIV/AIDS alcohol optimal control ABC strategy treatment; relapse
G. Mwanga, G., & Ongodia Kyambogo, E. (2020). Modelling Optimal Control of Heavy Alcohol Consumption on the Transmission Dynamics of HIV/AIDS. Journal of Humanities &Amp; Social Science (JHSS), 9(2). https://doi.org/10.56279/jhss.v9i2.49
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
References
  1. Agusto, F. B. 2009. Application of Optimal Control to the Epidemiology of HIV-Malaria Co-infection.
  2. Advances in Disease Epidemiology, 2012(81): 141–170.
  3. Agusto, F. B. & K. O. Okosun. 2010. Optimal Seasonal Biocontrol for Eichhornia Crassipes. International
  4. Journal of Biomathematics, 3(3): 383–397. https://doi.org/ 10.1142/ S1793 5245 10001021
  5. Beaglehole, R., R. Bonita, R. Horton, C. Adams, G. Alleyne, P. Asaria, …, … J. Watt. 2011. Priority
  6. Actions for the Non-communicable Disease Crisis. The Lancet, 377(9775): 1438–1447.
  7. https://doi.org/10.1016/S0140-6736(11)60393-0
  8. Berman, A. & R. J. Plemmons, 1994. Nonnegative Matrices in the Mathematical Sciences. In Society
  9. for Industrial and Applied Mathematics.
  10. Bhunu, C. P. 2012. A mathematical Analysis of Alcoholism. World Journal of Modelling and Simulation,
  11. (2): 124–134.
  12. Bhunu, C. P., W. Garira & G. Magombedze. 2009. Mathematical Analysis of a Two Strain HIV/AIDS
  13. model With Antiretroviral Treatment. Acta Biotheoretica, 57(3), 361–381.
  14. Birkhoff, G. & G.-C. Rota. 1989. Ordinary Differential Equations (4th ed.). John Wiley and Sons.
  15. Bonyah, E., M. A. Khan, K. O. Okosun & J. F. Gómez-Aguilar. 2019. Modelling the Effects of Heavy
  16. Alcohol Consumption on the Transmission Dynamics of gonorrhea With Optimal Control.
  17. Mathematical Biosciences, 309(December 2018): 1–11. https://doi.org/10.1016/j.mbs.2018.12.015:
  18. Braithwaite, R. S., K. A Nucifora,., J. Kessler, C. Toohey, S. M. Mentor, L. M. Uhler, M. S. Roberts &
  19. K. Bryant, 2014. Impact of Interventions Targeting Unhealthy Alcohol Use in Kenya on HIV
  20. Transmission and AIDS-Related Deaths. Alcoholism: Clinical and Experimental Research, 38(4),
  21. –1067. https://doi.org/10.1111/acer.12332
  22. Castens, V., F. Luginga, B. Shayo & C. Tolias. 2012. Alcohol Abuse in Urban Moshi, Tanzania.
  23. Castillo-Chavez, C., Z. Feng & W. Huang. 2002. On the Computation of R 0 and its Role on Global
  24. Stability. 229–250. https://doi.org/10.1007/978-1-4757-3667-0_13
  25. Fleming, W. H. & R. W. Rishel. 2012. Deterministic and Stochastic Optimal Control (Vol. 1). Springer
  26. Science & Business Media.
  27. Jasinski, D. R. & J. E. Henningfield. 1989. Human Abuse Liability Assessment by Measurement of
  28. Subjective and Physiological Effects. Testing for Abuse Liability of Drugs in Humans, 73–100.
  29. Joint United Nations Programme on HIV/AIDS & WHO. 2006. AIDS Epidemic Update, December
  30. World Health Organization.
  31. Joshi, H. R., S. Lenhart, M. Y. Li & L. Wang. 2006. Optimal Control Methods Applied to Disease
  32. Models. Contemporary Mathematics, 410: 187–208.
  33. Lutambi, A. M., M. A. Penny, T. Smith & N. Chitnis. 2013. Mathematical Modelling of Mosquito
  34. Dispersal in a Heterogeneous Environment. Mathematical Biosciences, 241(2): 198–216.
  35. https://doi.org/10.1016/j.mbs.2012.11.013
  36. Maksimov, V. I. 2013. On an Algorithm for Dynamic Reconstruction of the Input. Differential
  37. Equations, 49(1), 88–100. https://doi.org/10.1134/S0012266113010096
  38. Mushayabasa, S. & C. P. Bhunu. 2011. Modelling the Effects of Heavy Alcohol Consumption on the
  39. Transmission Dynamics of Gonorrhea. Nonlinear Dynamics, 66(4): 695–706. https://doi.org/
  40. 1007/s11071-011-9942-4
  41. Nuraini, N., R. Irawan & E. S. Zulkifli. 2011. Mathematical Modeling of HIV/AIDS Transmission among
  42. Injecting Drug Users with Methadone Therapy. Asian Trans. Basic Appl. Sci, 1: 10–15.
  43. Pandrea, I., K. I. Happel, A. M. Amedee, G. J. Bagby & S. Nelson. 2010. Alcohol’s Role in HIV
  44. Transmission and Disease Progression. Alcohol Research & Health.
  45. Sharp, P. M. & B. H. Hahn. 2011. Origins of HIV and the AIDS Pandemic. Cold Spring Harbor
  46. Perspectives in Medicine, 1(1). https://doi.org/10.1101/cshperspect.a006841
  47. Steen, R., T. E. Wi, A. Kamali & F. Ndowa. 2009. Control of Sexually Transmitted Infections and
  48. Prevention of HIV Transmission: Mending a Fractured Paradigm. Bulletin of the World Health
  49. Organization, 87: 858–865.
  50. Thomas, G. & E. M. Lungu. 2009. The Influence of Heavy Alcohol Consumption on HIV Infection and
  51. Progression. Journal of Biological Systems, 17(04): 685–712.
  52. Van Den Driessche, P. & J. Watmough. 2002. Reproduction Numbers and Sub-threshold Endemic
  53. Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180(1–
  54. , 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6.
Read More
Author biographies is not available.
Download this PDF file
Statistic
Read Counter : 68