The paper analyzes a model of immune system developed by different authors (Perelson, De Beer, 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.

Stable state analysis of an immune network model / G. C., Castellani; Giberti, Claudio; C., Franceschi; F., Bersani. - In: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING. - ISSN 0218-1274. - STAMPA. - 8(6):(1998), pp. 1285-1301.

Stable state analysis of an immune network model

GIBERTI, Claudio;
1998

Abstract

The paper analyzes a model of immune system developed by different authors (Perelson, De Beer, 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.
8(6)
1285
1301
Stable state analysis of an immune network model / G. C., Castellani; Giberti, Claudio; C., Franceschi; F., Bersani. - In: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS IN APPLIED SCIENCES AND ENGINEERING. - ISSN 0218-1274. - STAMPA. - 8(6):(1998), pp. 1285-1301.
G. C., Castellani; Giberti, Claudio; C., Franceschi; F., Bersani
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/612500
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact