Immune network behavior. I: From stationary states to limit cycle oscillations

DOI10.1007/BF02460672zbMath0797.92014WikidataQ52405877 ScholiaQ52405877MaRDI QIDQ2366765

Ioannis G. Kevrekidis, Alan S. Perelson, Rob J. de Boer

Publication date: 23 August 1993

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

symmetrystabilityequilibrium pointssteady statesimmune systems\(B\) cell clonesidiotypic interaction

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Physiology (general) (92C30)

Related Items (14)

A mathematical design of vector vaccine against autoimmune disease ⋮ Immune network behavior. II: From oscillations to chaos and stationary states ⋮ Immune networks modeled by replicator equations ⋮ Memory capacity in large idiotypic networks ⋮ Global dynamics of B cells and anti-idiotipic B cells and its application to autoimmunity ⋮ Frustration induced chaos in a system of coupled ODE's ⋮ Dynamical properties of autoimmune disease models: tolerance, flare-up, dormancy ⋮ The role of positive feedback loops involving anti-dsDNA and anti-anti-dsDNA antibodies in autoimmune glomerulonephritis ⋮ Modeling immune complex-mediated autoimmune inflammation ⋮ Immune response towards growing- and auto-antigen in an idiotypic network model ⋮ Stable State Analysis of an Immune Network Model ⋮ A Cayley tree immune network model with antibody dynamics ⋮ Memory in idiotypic networks due to competition between proliferation and differentiation ⋮ Complex behaviours of AB model describing idiotypic network

Cites Work

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• Memory but no suppression in low-dimensional symmetric idiotypic networks
• Unreasonable implications of reasonable idiotypic network assumptions
• Receptor clustering on a cell surface. I. Theory of receptor cross- linking by ligands bearing two chemically identical functional groups
• Approximate solution of a model of biological immune responses incorporating delay
• Receptor clustering on a cell surface. III. Theory of receptor cross- linking by multivalent ligands: Description by ligand states
• Modeling immune reactivity in secondary lymphoid organs
• Immune network behavior. II: From oscillations to chaos and stationary states

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