A delay differential equation model for tumor growth

J Math Biol. 2003 Sep;47(3):270-94. doi: 10.1007/s00285-003-0211-0. Epub 2003 May 15.


We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Animals
  • Antineoplastic Agents / therapeutic use*
  • Cell Cycle / drug effects
  • Cell Death / immunology
  • Cell Division / drug effects
  • Computer Simulation
  • Humans
  • Immune System / drug effects
  • Immune System / immunology
  • Mitosis / drug effects
  • Models, Biological*
  • Neoplasms / drug therapy*
  • Neoplasms / immunology
  • Neoplasms / pathology
  • T-Lymphocytes, Cytotoxic / drug effects
  • T-Lymphocytes, Cytotoxic / immunology


  • Antineoplastic Agents