Global Sensitivity Analysis for a Chronic Myelogenous Leukemia Model

  • Gabriel DimitriuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)


The goal of this paper is to carry out a global sensitivity analysis applied to a mathematical model for chronic myelogenous leukemia (CML) dynamics with T cell interaction. The interaction mechanism between naïve T cells, effector T cells, and CML cancer cells in the body is modeled by a system of ordinary differential equations which defines rates of variation for the three cell populations. We explain how to globally analyse the sensitivity of this complex system by means of two graphical objects: the sensitivity heat map and the parameter sensitivity spectrum.


  1. 1.
    Afenya, E., Calderón, C.: Diverse ideas on the growth kinetics of disseminated cancer cells. Bull. Math. Biol. 62, 527–542 (2000)CrossRefGoogle Scholar
  2. 2.
    Daescu, D.N., Navon, I.M.: Sensitivity analysis in nonlinear variational data assimilation: theoretical aspects and applications. In: Farago, I., Zlatev, Z. (eds.) Advanced Numerical Methods for Complex Environmental Models: Needs and Availability, pp. 1–16. Bentham Science Publishers (2013)Google Scholar
  3. 3.
    Dimitriu, G.: Determination of the optimal inputs for an identification problem using sensitivity analysis. In: Proceedings of the Second International Symposium on Sensitivity Analysis of Model Output (SAMO), Venice, 19–22 April 1998, pp. 99–102 (1998)Google Scholar
  4. 4.
    Dimitriu, G.: Numerical approximation of the optimal inputs for an identification problem. Intern. J. Comput. Math. 70, 197–209 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dimitriu, G.: Convergence rate for a convection parameter identified using Tikhonov regularization. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds.) NAA 2000. LNCS, vol. 1988, pp. 246–252. Springer, Heidelberg (2001). Scholar
  6. 6.
    Dimitriu, G.: Identifiability and Sensitivity Analyses for a Chronic Myelogenous Meukemia Model with \(T\) Cell Interaction. In: Proceedings of the IEEE International Conference ICSTCC, Sinaia, 19–21 October 2017, pp. 704–710 (2017)Google Scholar
  7. 7.
    Dimitriu, G., Boiculese, V.L.: Sensitivity study for a SEIT epidemic model. In: Proceedings of the 5th IEEE International Conference on e-Health and Bioengineering, Iaşi, 19–21 November 2015Google Scholar
  8. 8.
    Dimitriu, G., Moscalu, M., Boiculese, V.L.: A local sensitivity study for an activated \(T\)-cell model. In: Proceedings of the International Conference on e-Health and Bioengineering, Sinaia, 22–24 June 2017Google Scholar
  9. 9.
    Dimitriu, G., Lorenzi, T., Ştefănescu, R.: Evolutionary dynamics of cancer cell populations under immune selection pressure and optimal control of chemotherapy. Math. Model. Nat. Phenom. 9(04), 88–104 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Domijan, M., Brown, P., Shulgin, B., Rand, D.: Using PeTTSy, Perturbation Theory Toolbox for Systems. Warwick Systems Biology CentreGoogle Scholar
  11. 11.
    Georgescu, P., Hsieh, Y.-H.: Global stability for a virus dynamics model with nonlinear incidence of infection and removal. SIAM J. Appl. Math. 67(2), 337–353 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kalaba, R., Spingarn, K.: Control, Identification, and Input Optimization. Plenum Press, New York (1982)CrossRefGoogle Scholar
  13. 13.
    Kirschner, D., Panetta, J.C.: Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37, 235–252 (1998)CrossRefGoogle Scholar
  14. 14.
    Li, Z.: Sensitivity analysis approaches applied to systems biology models. IET Syst. Biol. 5(6), 336–346 (2011)CrossRefGoogle Scholar
  15. 15.
    Moore, H., Li, N.K.: A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. J. Theor. Biol. 227, 513–523 (2004)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pannell, D.J.: Sensitivity analysis of normative economic models: theoretical framework and practical strategies. Agric. Econ. 16(2), 139–152 (1997)CrossRefGoogle Scholar
  17. 17.
    Robert, C.P., Casella, G.: Monte Carlo Statistical Methods. Springer, New York (2004). Scholar
  18. 18.
    Saltelli, A., Campolongo, F., Cariboni, J., et al.: Global Sensitivity Analysis: The Primer. Wiley-Interscience, Chichester (2008)zbMATHGoogle Scholar
  19. 19.
    Saltelli, A., Ratto, M., Tarantola, S., Campolongo, F.: Sensitivity analysis for chemical models. Chem. Rev. 105(7), 2811–2827 (2005)CrossRefGoogle Scholar
  20. 20.
    Sellier, J.M., Dimov, I.: A sensitivity study of the Wigner Monte Carlo method. J. Comput. Appl. Math. 277, 87–93 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1–3), 271–280 (2001)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Steel, G.G.: Growth of Kinetic Tumors. Oxford University Press, Oxford (1977)Google Scholar
  23. 23.
    Zhang, H., Xia, J., Georgescu, P.: Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay. Nonlinear Anal. Model. Control 22(1), 64–83 (2017)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Medical Informatics and BiostatisticsUniversity of Medicine and Pharmacy Grigore T. PopaIaşiRomania

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