Delay-induced oscillatory dynamics of tumour-immune system interaction

Alberto d'Onofrio, Francesca Gatti, Paola Cerrai, Luca Freschi

Research output: Contribution to journalArticlepeer-review


The aim of this work on tumour-immune system (T-IS) interaction is to assess the effect of delays concerning the stimulation of the immune system by tumour cells, as well as the interplay between antitumour immunotherapies and delays. After defining a new family of super-macroscopic models for the T-IS interaction, we introduce a constant delay in the proliferation of immune effectors. We then investigate, both analytically and by means of simulations, the stability of equilibria and the onset of sustained oscillations through Hopf bifurcations. Both constant and exponentially distributed lags are considered. In particular, in the case of periodically varying immunotherapies we show that nonlinear resonances and chaos may arise, although for parameters slightly outside the range of biological realism.

Original languageEnglish
Pages (from-to)572-591
Number of pages20
JournalMathematical and Computer Modelling
Issue number5-6
Publication statusPublished - Mar 2010


  • Delay-differential equations
  • Immune system
  • Oncology

ASJC Scopus subject areas

  • Computer Science Applications
  • Modelling and Simulation


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