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 language | English |
|---|---|
| Pages (from-to) | 572-591 |
| Number of pages | 20 |
| Journal | Mathematical and Computer Modelling |
| Volume | 51 |
| Issue number | 5-6 |
| DOIs | |
| Publication status | Published - Mar 2010 |
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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 journal › Article
}
TY - JOUR
T1 - Delay-induced oscillatory dynamics of tumour-immune system interaction
AU - d'Onofrio, Alberto
AU - Gatti, Francesca
AU - Cerrai, Paola
AU - Freschi, Luca
PY - 2010/3
Y1 - 2010/3
N2 - 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.
AB - 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.
KW - Delay-differential equations
KW - Immune system
KW - Oncology
UR - http://www.scopus.com/inward/record.url?scp=74149087236&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=74149087236&partnerID=8YFLogxK
U2 - 10.1016/j.mcm.2009.11.005
DO - 10.1016/j.mcm.2009.11.005
M3 - Article
AN - SCOPUS:74149087236
VL - 51
SP - 572
EP - 591
JO - Mathematical and Computer Modelling
JF - Mathematical and Computer Modelling
SN - 0895-7177
IS - 5-6
ER -