Journal of Mathematical Biology

, Volume 37, Issue 3, pp 235–252

Modeling immunotherapy of the tumor – immune interaction

  • Denise Kirschner
  • John Carl Panetta

DOI: 10.1007/s002850050127

Cite this article as:
Kirschner, D. & Panetta, J. J Math Biol (1998) 37: 235. doi:10.1007/s002850050127


 A number of lines of evidence suggest that immunotherapy with the cytokine interleukin-2 (IL-2) may boost the immune system to fight tumors. CD4+ T cells, the cells that orchestrate the immune response, use these cytokines as signaling mechanisms for immune-response stimulation as well as lymphocyte stimulation, growth, and differentiation. Because tumor cells begin as ‘self’, the immune system may not respond in an effective way to eradicate them. Adoptive cellular immunotherapy can potentially restore or enhance these effects. We illustrate through mathematical modeling the dynamics between tumor cells, immune-effector cells, and IL-2. These efforts are able to explain both short tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated.

Key words: ImmunotherapyTumorCytokineModelingInterleukin-2Ordinary differential equations

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Denise Kirschner
    • 1
  • John Carl Panetta
    • 2
  1. 1.Department of Microbiology and Immunology, The University of Michigan Medical School, Ann Arbor, MI 48109-0620, USAUS
  2. 2.School of Science, Penn State Erie, The Behrend College, Station Road, Erie, PA 16563-0203, USA. e-mail: