Journal of Mathematical Biology

, Volume 47, Issue 3, pp 270–294 | Cite as

A delay differential equation model for tumor growth

  • Minaya VillasanaEmail author
  • Ami Radunskaya


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.


 Cycle-phase-specific drugs Delay differential equations Tumor growth 


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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Departamento de Cómputo Científico y EstadísticaUniversidad Simón BolivarVenezuelaUSA
  2. 2.Mathematics DepartmentPomona CollegeUSA

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