Call for Paper - December 2019 Edition
IJCA solicits original research papers for the December 2019 Edition. Last date of manuscript submission is November 20, 2019. Read More

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

Print
PDF
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
Omar Zakary, Mostafa Rachik, Ilias Elmouki
10.5120/ijca2016908030

Omar Zakary, Mostafa Rachik and Ilias Elmouki. Article: On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control. International Journal of Computer Applications 133(9):1-6, January 2016. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {Omar Zakary and Mostafa Rachik and Ilias Elmouki},
	title = {Article: On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control},
	journal = {International Journal of Computer Applications},
	year = {2016},
	volume = {133},
	number = {9},
	pages = {1-6},
	month = {January},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

In this work, a mathematical model for studying the impact of awareness programs on HIV/AIDS outbreak is proposed. The main idea is that people who are susceptible to infection can prevent it, if they are aware how the disease spreads and its consequences, and also the measures to control it. Various forms of communication media, educational, heath institutions and non-governmental organizations play a significant role to promote HIV/AIDS awareness amongst the most concerned people, namely couples and senior secondary school children. The developed HIV model is inspired from the classical SIR epidemic model where a control function is introduced to represent the effectiveness of an awareness program. The obtained optimal control, is characterized in terms of the optimality system, based on Pontryagin

References

  1. Ayiro, L. (2012). HIV/AIDS and its Impact on Education in Sub-Saharan Africa: Policy Initiatives and Challenges. The Impact of HIV/AIDS on Education Worldwide, 18, 126.
  2. FACT SHEET (2014). GLOBAL STATISTICS. http://www.unaids.org
  3. MDG 6: 15 YEARS, 15 LESSONS OF HOPE FROM THE AIDS RESPONSE FACT SHEET (2014). GLOBAL STATISTICS. http://www.unaids.org
  4. GLOBAL AIDS RESPONSE PROGRESS REPORTING (2014). Construction of Core indicators for monitoring the 2011 united nations Political declaration on HiV and Aids. http://www.unaids.org
  5. The GAP REPORT (2014). http://www.unaids.org
  6. PROGRESS REPORT ON THE GLOBAL PLAN (2014). Towards the elimination of new HIV infections among children by 2015 and keeping their mothers alive. http://www.unaids.org
  7. Africa Renewal. (2004). Women: the face of AIDS in Africa. United Nations Department of Public Information, 18.
  8. Ongaga, K., & Ombonga, M. (2012). HIV/AIDS Education Programs in Kenya: Contexts of Implementation in Secondary Schools in Kisii County. The Impact of HIV/AIDS on Education Worldwide, 18, 2756.
  9. Aggleton, P., Yankah, E., & Crewe, M. (2011). Education and HIV/AIDS-30 years on. AIDS Education and Prevention, 23(6), 495-507.
  10. Crewe, M. (2004). A PEP talk too far: The power of AIDS education. Plenary presentation given at the 15th International AIDS Conference, Bangkok, Thailand. Retrieved from http://www.csa.za.org/resources/catview/76-hivand- education
  11. UNAIDS. (2002). Global coalition on women and AIDS. Global campaign for Education Global AIDS Alliance. Geneva, Switzerland.
  12. Akala, F.A., & Semini, I. (2010). Characterizing the HIV/AIDS epidemic in the Middle East and North Africa: time for strategic action. World Bank Publications.
  13. Bundy, D., Patrikios, A., Mannathoko, C., Tembon, A., Manda, S., Sarr, B., & Drake, L. (2010). Accelerating the education sector response to HIV: Five years of experience from Sub-Saharan Africa. World Bank Publications.
  14. Cataln, J., Sherr, L., & Hedge, B. (1997). The impact of AIDS: psychological and social aspects of HIV infection. Taylor & Francis.
  15. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. (1962). The mathematical theory of optimal processes (International series of monographs in pure and applied mathematics). Interscience, New York.
  16. Fleming, W., & Rishel, R. (1975). Deterministic and Sochastic Optimal Control Springer-Verlag.
  17. Kamien, M. I., & Schwartz, N. L. (1991). Dynamic optimisation. The calculus of variations and optimal control in economics and management (second edition) North Holland, New York.
  18. Jung, E., Lenhart, S., & Feng, Z. (2002). Optimal control of treatments in a two-strain tuberculosis model. Discrete and Continuous Dynamical Systems Series B, 2(4), 473-482.
  19. Moualeu, D. P.,Weiser, M., Ehrig, R., & Deuflhard, P. (2015). Optimal control for a tuberculosis model with undetected cases in Cameroon. Communications in Nonlinear Science and Numerical Simulation, 20(3), 986-1003.
  20. Kim, B. N., Nah, K., Chu, C., Ryu, S. U., Kang, Y. H., & Kim, Y. (2012). Optimal control strategy of Plasmodium vivax malaria transmission in Korea. Osong Public Health and Research Perspectives, 3(3), 128-136.
  21. Joshi, H. R. (2002). Optimal control of an HIV immunology model. Optimal control applications and methods, 23(4), 199- 213.
  22. Fister, K. R., Lenhart, S., & McNally, J. S. (1998). Optimizing chemotherapy in an HIV model. Electronic Journal of Differential Equations, 1998(32), 1-12.
  23. Kwon, H. D., Lee, J., & Yang, S. D. (2012). Optimal control of an age-structured model of HIV infection. Applied Mathematics and Computation, 219(5), 2766-2779.
  24. Zakary, O., Rachik, M. and Elmouki, I. (2015). On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model. International Journal of Computer Applications, 127(12), pp.1-10.

Keywords

HIV/AIDS model, SIR model, Optimal control, Awareness program