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

Bull Math Biol. 1994 Mar;56(2):295-321. doi: 10.1007/BF02460644.


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 seen in 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 measured in 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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Animals
  • Cytotoxicity, Immunologic*
  • Kinetics
  • Lymphoma, B-Cell / immunology*
  • Lymphoma, B-Cell / pathology*
  • Mathematics*
  • Mice
  • Models, Biological*
  • T-Lymphocytes, Cytotoxic / immunology*
  • Time Factors