Search research articles

Search research articles

Related Experiment Videos

A basic mathematical model of the immune response.

H. Mayer¹, K. S. Zaenker, U. An Der Heiden

¹Institute of Immunology and Institute of Mathematics, University of Witten/Herdecke, Stockumer Strasse 10, D-58448 Witten, GermanyInstitute of Immunology, University of Witten/Herdecke, Stockumer Strasse 10, D-58448 Witten, GermanyInstitute of Mathematics, University of Witten/Herdecke, Stockumer Strasse 10, D-58448 Witten, Germany.

Chaos (Woodbury, N.Y.)

|March 1, 1995

Summary

This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026

Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026

Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026

Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026

Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026

Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026

See all related articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

This study models immune system dynamics using differential equations, revealing how nonlinear interactions create diverse immune responses. The model predicts thresholds for pathogen elimination and explains immune system failure and paradoxical outcomes, including benefits from additional challenges.

Area of Science:

Immunology
Mathematical Biology
Systems Biology

Background:

Immune system interactions with targets (pathogens, tumor cells) are dynamic processes.
Understanding these dynamics is crucial for explaining immune responses and failures.

Purpose of the Study:

To model the dynamic interaction between the immune system and target populations.
To explore how nonlinear interaction rules generate diverse immune responses.
To explain observed immunological states and phenomena.

Main Methods:

A system of two ordinary differential equations was used to model immune dynamics.
The model incorporates nonlinear interaction rules between immune cells and targets.
Solutions were analyzed to identify different immune states and response patterns.

Related Experiment Videos

Main Results:

The model replicates "virgin state," "immune state," and "state of tolerance."
It successfully simulates primary and secondary immune responses.
A threshold for pathogen/tumor cell elimination was predicted, alongside conditions for immune system failure and paradoxical outcomes like enhanced survival despite increased immunity.

Conclusions:

The idealized model demonstrates how simple nonlinear rules generate complex immune behaviors.
It provides a framework for understanding immune system thresholds, failures, and paradoxical responses.
The model suggests potential therapeutic insights, including benefits from additional target challenges and the possibility of chaotic dynamics under pulsed stimulation.