Delay-induced oscillatory dynamics of tumour-immune system interaction

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

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

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
Volume51
Issue number5-6
DOIs
Publication statusPublished - Mar 2010

Fingerprint

Immune system
Immune System
Immunotherapy
Tumors
Tumor
Interaction
Nonlinear Resonance
Hopf bifurcation
Stability of Equilibria
Proliferation
Chaos theory
Hopf Bifurcation
Chaos
Cells
Oscillation
Cell
Range of data
Simulation
Model

Keywords

  • Delay-differential equations
  • Immune system
  • Oncology

ASJC Scopus subject areas

  • Computer Science Applications
  • Modelling and Simulation

Cite this

Delay-induced oscillatory dynamics of tumour-immune system interaction. / d'Onofrio, Alberto; Gatti, Francesca; Cerrai, Paola; Freschi, Luca.

In: Mathematical and Computer Modelling, Vol. 51, No. 5-6, 03.2010, p. 572-591.

Research output: Contribution to journalArticle

d'Onofrio, Alberto ; Gatti, Francesca ; Cerrai, Paola ; Freschi, Luca. / Delay-induced oscillatory dynamics of tumour-immune system interaction. In: Mathematical and Computer Modelling. 2010 ; Vol. 51, No. 5-6. pp. 572-591.
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