# AIDS환자 치료를 위한 점진적 약물감소기법에 감염속도상수가 미치는 영향

• 이강현 (숭실대 공대 전기공학부) ;
• 조남훈 (숭실대 공대 전기공학부)
• Published : 2007.01.01

#### Abstract

In this paper, we study the influence of infection ratio on gradual reduction of drug dose for the five state HIV infection model that explicitly includes the population of the virus. We first compute all equilibrium points of the model and investigate the stabilities of them. As a result, a bifurcation diagram is obtained which shows a change in the equilibrium points, or in their stability properties, as the drug effect $\eta$ is varied from 0 to 1(alternatively, drug dose is changed from 1 to 0). Based on the bifurcation diagram, we show that the gradual reduction of drug dose can be applied for the treatment of AIDS patients. Moreover, we analyze the influence of the variation of infection ratio on the gradual reduction treatment. Computer simulation results are also presented to validate the proposed results.

#### References

1. ﻿D. Wodarz and M.A. Nowak, 'Specific therapy regimes could lead to long-term immunological control of HN,' PNAS, vol. 96, pp. 14464-14469, December 1999 https://doi.org/10.1073/pnas.96.25.14464
2. ﻿D. Wodarz and M.A. Nowak, 'Mathematical models of HIV pathogenesis and treatment,' BioEssays, vol. 24, pp. 1178-1187, Wiley Periodicals, 2002
3. ﻿H. Shim, S.J. Han, C.C. Chung, SW. Nam, and J.H. Seo, 'Optimal Scheduling of Drug Treatment for HIV Infection: Continuous Dose Control and Receding Horizon Control,' International Journal of Control, Automation, and Systems, Vol. 1, No.3, pp.401-407, Sep., 2003
4. H.J. Chang, H. Shim and J.H. Seo, 'Control of Immune Response of HN Infection Model by Gradual Reduction of Drug Dose,' 43rd IEEE Coriference on Decision and Control, Vol. 1, pp.1048-1054, Dec., 2004
5. J.S. James, 'Human Retroviruses and Related Infections,' Major U.S. Scientific AIDS Conference, Feb. 1995. (Available at http://www.aids.org/atn/a-216-0l.htmㅣ.)
6. ﻿Purves, Life: The Science of Biology, 7th Ed, Freeman, 2004
7. 김세종, 면역학길라잡이, 고려의학, 2000
8. ﻿D. Wodarz, 'Helper-dependent vs. helper-independent CTL responses in HN infection: implications for drug therapy and resistance,' J. Theor. BioI., vol. 213, pp. 447-459, August 2001 https://doi.org/10.1006/jtbi.2001.2426
9. ﻿R. Zurakowski and AR. Teel, 'Enhancing immune response to HIV infection using MPC-based treatment scheduling,' In proceedings of American Control Conference, Denver, 2003
10. S. Kubiak, H. Lehr, R. Levy, T. Moeller, A. Parker, and E. Swin, 'Modeling control of HN infection through structured treatment interruptions with recommendations for experimental protocol,' CRSC Technical Report (CRSC-TROl-27), 2001
11. ﻿H. Shim, H.J. Chang and J.H. Seo, 'Non -vanishing basin of attraction with respect to a parametric variation and center manifold,' Conference on Decision and Control (CDC), 2004
12. ﻿C. A. Janeway, Irnmunobiology: The immune system in health and disease, 6th Ed, Garland Pub, 2004