### Abstract

The paper analyzes a model of immune system developed by different authors (Perelson De Boer, Weisbuch and others). The model describes interactions among B-lymphocytes. It does not consider antibodies as interaction intermediaries, although it uses a typical activation curve. The relevant parameters are: an influx term, a threshold value, a proliferation rate, and a decay parameter. The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases. When the influx term is neglected the stationary states are obtained analytically and their stability is discussed Moreover, it is discussed how the stable solutions can be considered as "selective states", that is, with only one high idiotypic concentration, when we suppose a complete connectivity.

Original language | English |
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Pages (from-to) | 1285-1301 |

Number of pages | 17 |

Journal | International Journal of Bifurcation and Chaos |

Volume | 8 |

Issue number | 6 |

Publication status | Published - Jun 1998 |

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### ASJC Scopus subject areas

- General
- Applied Mathematics

### Cite this

*International Journal of Bifurcation and Chaos*,

*8*(6), 1285-1301.

**Stable state analysis of an immune network model.** / Castellani, G. C.; Giberti, C.; Franceschi, C.; Bersani, F.

Research output: Contribution to journal › Article

*International Journal of Bifurcation and Chaos*, vol. 8, no. 6, pp. 1285-1301.

}

TY - JOUR

T1 - Stable state analysis of an immune network model

AU - Castellani, G. C.

AU - Giberti, C.

AU - Franceschi, C.

AU - Bersani, F.

PY - 1998/6

Y1 - 1998/6

N2 - The paper analyzes a model of immune system developed by different authors (Perelson De Boer, Weisbuch and others). The model describes interactions among B-lymphocytes. It does not consider antibodies as interaction intermediaries, although it uses a typical activation curve. The relevant parameters are: an influx term, a threshold value, a proliferation rate, and a decay parameter. The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases. When the influx term is neglected the stationary states are obtained analytically and their stability is discussed Moreover, it is discussed how the stable solutions can be considered as "selective states", that is, with only one high idiotypic concentration, when we suppose a complete connectivity.

AB - The paper analyzes a model of immune system developed by different authors (Perelson De Boer, Weisbuch and others). The model describes interactions among B-lymphocytes. It does not consider antibodies as interaction intermediaries, although it uses a typical activation curve. The relevant parameters are: an influx term, a threshold value, a proliferation rate, and a decay parameter. The study of the n-dimensional extension of the model and a bifurcation analysis of the stationary states with respect to the influx parameter show that the influx value for which biologically acceptable solutions exist decreases as n increases. When the influx term is neglected the stationary states are obtained analytically and their stability is discussed Moreover, it is discussed how the stable solutions can be considered as "selective states", that is, with only one high idiotypic concentration, when we suppose a complete connectivity.

UR - http://www.scopus.com/inward/record.url?scp=0032093452&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032093452&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032093452

VL - 8

SP - 1285

EP - 1301

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 6

ER -