Advertisement

HIV Therapy via Noncomputational Optimal Control Approach

  • Bingo Wing-Kuen LingEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

In this chapter, we numerically show that the dynamics of the HIV system is sensitive to both the initial condition and the system parameters. These phenomena imply that the system is chaotic and exhibits a bifurcation behavior. To control the system, we propose to initiate an HIV therapy based on both the concentration of the HIV-1 viral load and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population. If the concentration of the HIV-1 viral load is higher than a threshold, then the first type of therapy will be applied. If the concentration of the HIV-1 viral load is lower than or equal to the threshold and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population is greater than another threshold, then the second type of therapy will be applied. Otherwise, no therapy will be applied. The advantages of the proposed control strategy are that the therapy can be stopped under certain conditions, while the state variables of the overall system is asymptotically stable with fast convergent rate, the concentration of the controlled HIV-1 viral load is monotonic decreasing, as well as the positivity constraint of the system states and that of the dose concentration is guaranteed to be satisfied. Computer numerical simulation results are presented for an illustration.

References

  1. 1.
    Craig, I.K., Xia, X., Venter, J.W.: Introducing HIV/AIDS education into the electrical engineering curriculum at the university of Pretoria. IEEE Trans. Edu. 47(1), 65–73 (2004)CrossRefGoogle Scholar
  2. 2.
    Filter, R.A., Xia, X., Gray, C.M.: Dynamic HIV/AIDS parameter estimation with application to a vaccine readiness study in Southern Africa. IEEE Trans. Biomed. Eng. 52(5), 784–791 (2005)CrossRefGoogle Scholar
  3. 3.
    Xia, X., Moog, C.H.: Identifiability of nonlinear systems with application to HIV/AIDS models. IEEE Trans. Automat. Contr. 48(2), 330–336 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hammond, B.J.: Quantitative study of the control of HIV-1 gene expression. J. Theor. Biol. 163, 199–221 (1993)CrossRefGoogle Scholar
  5. 5.
    Wein, L.M., Zenios, S.A., Nowak, M.A.: Dynamic multidrug therapies for HIV: a control theoretic approach. J. Theor. Biol. 185, 15–29 (1997)CrossRefGoogle Scholar
  6. 6.
    De Boer, R.J., Perelson, A.S.: Target cell limited and immune control models of HIV infection: a compression. J. Theor. Biol. 190, 201–214 (1998)CrossRefGoogle Scholar
  7. 7.
    Wein, L.M., D’Amato, R.M., Perelson, A.S.: Mathematical analysis of antiretroviral therapy aimed at HIV-1 eradication or maintenance of low viral loads. J. Theor. Biol. 192, 81–98 (1998)CrossRefGoogle Scholar
  8. 8.
    Dixit, N.M., Perelson, A.S.: Complex patterns of viral load decay under antiretroviral therapy: influence of pharmacokinetics and intracellular delay. J. Theor. Biol. 226, 95–109 (2004)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Strfford, M.A., Corey, L., Cao, Y., Daar, E.S., Ho, D.D., Perelson, A.S.: Modeling plasma virus concentration during primary HIV infection. J. Theor. Biol. 203, 285–301 (2000)CrossRefGoogle Scholar
  10. 10.
    Fishman, M.A., Perelson, A.S. Th1/Th2 cross regulation. J. Theor. Biol. 170, 25–56 (1994)CrossRefGoogle Scholar
  11. 11.
    Essunger, P., Perelson, A.S.: Modeling HIV infection of CD4+ T-cell subpopulations. J. Theor. Biol. 170, 367–391 (1994)CrossRefGoogle Scholar
  12. 12.
    Berry, R.M., Nowak, M.A. Defective escape mutants of HIV. J. Theor. Biol. 171, 387–395 (1994)CrossRefGoogle Scholar
  13. 13.
    Lipsitch, M., Nowak, M.A.: The evolution of virulence in sexually transmitted HIV/AIDS. J. Theor. Biol. 174, 427–440 (1995)CrossRefGoogle Scholar
  14. 14.
    Nowak, M.A., May, R.M., Sigmund, K.: Immune responses against multiple epitopes. J. Theor. Biol. 175, 352–353 (1995)CrossRefGoogle Scholar
  15. 15.
    Courchamp, F., Pontier, D., Langlais, M., Artois, M.: Population dynamics of feline immunodeficiency virus within cat populations. J. Theor. Biol. 175, 553–560 (1995)CrossRefGoogle Scholar
  16. 16.
    Iwasa, Y., Michor, F., Nowak, M.A. Virus evolution within patients increases pathogenicity. J Theor. Biol. 232, 17–26 (2005)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Nowak, M.A., Bonhoeffer, S., Shaw, G.M., May, R.M.: Anti-viral drug treatment: dynamics of resistance in free virus and infected cell populations. J. Theor. Biol. 184, 203–217 (1997)CrossRefGoogle Scholar
  18. 18.
    Wodarz, D., Lloyd, A.L., Jansen, V.A.A., Nowak, M.A.: Dynamics of macrophage and T cell infection by HIV. J. Theor. Biol. 196, 101–113 (1999)CrossRefGoogle Scholar
  19. 19.
    Gilchrist, M.A., Coombs, D., Perelson, A.S.: Optimizing within-host viral fitness: infected cell lifespan and virion production rate. J. Theor. Biol. 229, 281–288 (2004)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Jafelice, R.M., Barros, L.C., Gomide, R.C.B.F.: Fuzzy set-based model to compute the life expectancy of HIV infected populations. IEEE Ann. Meet. Fuzzy Inform. Process. NAFIPS 1, 314–318 (2004)CrossRefGoogle Scholar
  21. 21.
    Ge, S.S., Tian, Z., Lee, T.H.: Nonlinear control of a dynamic model of HIV-1. IEEE Trans. Biomed. Eng. 52(3), 353–361 (2005)CrossRefGoogle Scholar
  22. 22.
    Campello de Souza, F.M.: Modeling the dynamics of HIV-1 and CD4 and CD8 lymphocytes. IEEE Eng. Med. Biol. 18(1), 21–24 (1999)Google Scholar
  23. 23.
    Jeffrey, A.M., Xia, X., Craig, I.K.: When to initiate HIV therapy: a control theoretic approach. IEEE Trans. Biomed. Eng. 50(11), 1213–1220 (2003)CrossRefGoogle Scholar
  24. 24.
    Brandt, M.E., Chen, G.: Feedback control of a biodynamical model of HIV-1. IEEE Trans. Biomed. Eng. 48(7), 754–759 (2001)CrossRefGoogle Scholar
  25. 25.
    Craig, I.K., Xia, X.: Can HIV/AIDS be controlled? Applying control engineering concepts outside traditional fields. IEEE Contr. Syst. Mag. 25(1), 80–83 (2005)CrossRefGoogle Scholar
  26. 26.
    Ko, J.H., Kim, W.H., Chung, C.C.: Optimized structured treatment interruption for HIV therapy and its performance analysis on controllability. IEEE Trans. Biomed. Eng. 53(3), 380–386 (2006)CrossRefGoogle Scholar
  27. 27.
    Arora, D., Skliar, M., Roemer, R.B.: Minimum-time thermal dose control of thermal therapies. IEEE Trans. Biomed. Eng. 52(2), 191–200 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of EngineeringUniversity of LincolnLincolnUK

Personalised recommendations