Stochastic Modeling of Temporal Variability of HIV-1 Population

  • Ilia Kiryukhin
  • Kirill Saskov
  • Alexander Boukhanovsky
  • Wilco Keulen
  • Charles Boucher
  • Peter M. A. Sloot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2657)


A multivariate stochastic model for describing the dynamics of complex non-numerical ensembles, such as observed in Human Immunodeficiency Virus (HIV) genome, is developed. This model is based on principle component analyses for numberized variables. The model coefficients are presented in the terms of deterministic trends with correlated lags. The results indicate that we may use this model in short-term forecast of HIV evolution, for evaluation of HIV drug resistance and for testing and validation of diagnostic expert rules. The model also reproduces the specific shape of the bi-modal distribution for the mutations number.


Human Immunodeficiency Virus Temporal Variability Cellular Automaton Empirical Orthogonal Function Principle Component Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Durant J, Clevenbergh P, Halfon P, et al. Drug-resistance genotyping in HIV-1 therapy: the VIRADAPT randomised controlled trial. Lancet 1999; 353:21959.CrossRefGoogle Scholar
  2. 2.
    Baxter JD, Mayers DL, Wentworth DN, et al. A randomized study of antiretroviral management based on plasma genotypic antiretroviral resistance testing in patients failing therapy. CPCRA 046 study team for the Terry Beirn Community Programs for Clinical Research on AIDS. AIDS 2000; 14:F8393.Google Scholar
  3. 3.
    Zollner B, Feucht HH, Weitner L, Adam A, Laufs R. Drug-resistant genotyping in HIV-1 therapy. Lancet 1999; 354:112021.CrossRefGoogle Scholar
  4. 4.
    Maree AF, Keulen W, Boucher CA, De Boer RJ. Estimating relative fitness in viral competition experiments. J Virol 2000 Dec;74(23):11067–02.CrossRefGoogle Scholar
  5. 5.
    P.M.A. Sloot, F. Chen and C.A. Boucher: Cellular Automata Model of Drug Therapy for HIV Infection, in S. Bandini; B. Chopard and M. Tomassini, editors, 5th International Conference on Cellular Automata for Research and Industry, ACRI 2002, Geneva, Switzerland, October 9–11, 2002. Proceedings, in series Lecture Notes in Computer Science, vol. 2493, pp. 282–293. October 2002.Google Scholar
  6. 6.
    Little SJ, Holte S, Routy JP, Daar ES, Markowitz M, Collier AC, Koup RA, Mellors JW, Connick E, Conway B, Kilby M, Wang L, Whitcomb JM, Hellmann NS, Richman DD. Antiretroviral-drug resistance among patients recently infected with HIV. N Engl J Med 2002 Aug 8;347(6):385–94CrossRefGoogle Scholar
  7. 8.
    Mathematical Methods for DNA Sequences // Ed. M.S. Waterman. CRC Press Inc., Boca Raton, Florida, 1999.Google Scholar
  8. 9.
    Anderson T.W. An introduction to multivariate statistical analysis. John Wiley, NY, 1948.Google Scholar
  9. 10.
    Bartlett M.S. Multivariate analysis. J. Roy. Stat. Soc. Suppl. 9(B), 1947, 176–197.CrossRefMathSciNetGoogle Scholar
  10. 11.
    Brilinger D. Time series. Data analysis and theory. Holt, Renehart and Winston, Inc., New York, 1975.Google Scholar
  11. 12.
    Aivazyan S.A., Buchstaber V.M., Yenyukov I.S., Meshalkin L.D. Applied statistics. Classification and reduction of dimensionality. Finansy i statistica, Moscow, 1989, 608 p. (in Russian)Google Scholar
  12. 13.
    Johnson R.A., Wichern D.W. Applied multivariate statistical analysis. Prentice-Hall Internalional, Inc., London, 1992, 642 pp.zbMATHGoogle Scholar
  13. 14.
    Ogorodnikov V.A., Prigarin S.M. Numerical modelling of random processes and fields: algorithms and applications. VSP, Utrecht, the Netherlands, 1996, 240 p.zbMATHGoogle Scholar
  14. 15.
    Wolfe J.H. Pattern clustering for multivariate mixture analysis. Miltiv. Behav. Res., 1969, 22, pp. 165–170.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ilia Kiryukhin
    • 1
  • Kirill Saskov
    • 1
  • Alexander Boukhanovsky
    • 1
  • Wilco Keulen
    • 2
  • Charles Boucher
    • 3
  • Peter M. A. Sloot
    • 4
  1. 1.Institute for High Performance Computing and Information SystemsSt.PetersburgRussia
  2. 2.Virology NetworkUtrechtThe Netherlands
  3. 3.University Medical CenterUtrechtThe Netherlands
  4. 4.University of AmsterdamAmsterdamThe Netherlands

Personalised recommendations