Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis

Area of Science:

• Mathematical Biology
• Immunology
• Computational Science

Background:

• Chemotaxis plays a crucial role in immune cell function.
• Understanding immune cell dynamics is vital for treating infections and inflammatory diseases.

Purpose of the Study:

• To develop a minimal mathematical model for chemotaxis in the immune system.
• To analyze the stability and dynamics of immune cell-antigen interactions.
• To investigate the impact of chemotactic strength on immune responses.

Main Methods:

• A reaction-diffusion-advection system was formulated to model immune cell and antigen interactions.
• Analytical techniques including energy estimates and spectral analysis were employed.
• Numerical simulations utilized the finite volume and fractional step methods.

Main Results:

• The model predicts effective attraction of immune cells to infection sites.
• Conditions for stability and instability were determined based on chemotactic strength.
• Hypersensitivity was observed when chemotactic strength exceeded a critical threshold.

Conclusions:

• The mathematical model provides insights into immune cell recruitment via chemotaxis.
• Chemotactic strength is a key factor determining immune response effectiveness and potential hypersensitivity.
• The findings contribute to understanding immune system dynamics in infection and inflammation.