Stable state analysis of an immune network model

G. C. Castellani, C. Giberti, C. Franceschi, F. Bersani

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1285-1301
Number of pages17
JournalInternational Journal of Bifurcation and Chaos
Volume8
Issue number6
Publication statusPublished - Jun 1998

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Network Model
Stationary States
B Lymphocytes
Lymphocytes
Stable Solution
Immune system
Immune System
Bifurcation Analysis
Term
Proliferation
Threshold Value
Interaction
Antibody
Antibodies
n-dimensional
Activation
Connectivity
Chemical activation
Model
Decay

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Castellani, G. C., Giberti, C., Franceschi, C., & Bersani, F. (1998). Stable state analysis of an immune network model. 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.

In: International Journal of Bifurcation and Chaos, Vol. 8, No. 6, 06.1998, p. 1285-1301.

Research output: Contribution to journalArticle

Castellani, GC, Giberti, C, Franceschi, C & Bersani, F 1998, 'Stable state analysis of an immune network model', International Journal of Bifurcation and Chaos, vol. 8, no. 6, pp. 1285-1301.
Castellani, G. C. ; Giberti, C. ; Franceschi, C. ; Bersani, F. / Stable state analysis of an immune network model. In: International Journal of Bifurcation and Chaos. 1998 ; Vol. 8, No. 6. pp. 1285-1301.
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