Bulletin of Mathematical Biology

, Volume 56, Issue 2, pp 295–321 | Cite as

Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis

  • Vladimir A. Kuznetsov
  • Iliya A. Makalkin
  • Mark A. Taylor
  • Alan S. Perelson


We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.


Human Immunodeficiency Virus Effector Cell Phase Portrait Chimeric Mouse Dormant State 
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Copyright information

© Society for Mathematical Biology 1994

Authors and Affiliations

  • Vladimir A. Kuznetsov
    • 1
  • Iliya A. Makalkin
    • 1
  • Mark A. Taylor
    • 2
  • Alan S. Perelson
    • 2
  1. 1.Laboratory of Mathematical Immunobiophysics, Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia
  2. 2.Theoretical DivisionLos Alamos National LaboratoryLos AlamosU.S.A.

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