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Microfluidic Co-Culture Models for Dissecting the Immune Response in in vitro Tumor Microenvironments
Published on: April 30, 2021
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Oscillations in a tumor-immune system interaction model with immune response delay.
Zhaoxuan Huo1, Jicai Huang1, Yang Kuang2
1School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China.
Mathematical Medicine and Biology : a Journal of the IMA
|September 17, 2024
Summary
This study models tumor-immune system interactions with delayed responses. Time delays critically influence tumor equilibrium stability and can induce complex oscillations, impacting disease dynamics.
Area of Science:
- Mathematical Biology
- Immunology
- Dynamical Systems Theory
Background:
- Tumor-immune system dynamics are complex and influenced by response times.
- Understanding these interactions is crucial for developing effective cancer therapies.
- Previous models often simplify the immune response or time delays.
Purpose of the Study:
- To investigate the impact of immune response delay on tumor-immune system dynamics.
- To analyze the existence and stability of tumor equilibria under varying conditions.
- To explore bifurcations and complex oscillating patterns arising from time delays.
Main Methods:
- Development of a mathematical model incorporating a nonmonotonic immune response function and time delay.
- Analysis of tumor equilibria and their stability.
- Application of Hopf bifurcation theory (local and global) to identify critical delays and bifurcating solutions.
- Numerical simulations to validate theoretical findings and observe complex dynamics.
Main Results:
- The model exhibits one, two, or three tumor equilibria depending on conditions.
- Time delay affects the stability of the low tumor equilibrium, leading to local Hopf bifurcation at a critical delay.
- Periodic solutions (including relaxation oscillations and complex patterns) emerge due to time delays.
- Numerical simulations confirm theoretical predictions.
Conclusions:
- Immune response delay is a critical factor in tumor-immune system dynamics.
- Time delays can destabilize equilibria and generate complex, potentially detrimental, oscillations.
- The findings provide insights into the role of timing in immune surveillance and cancer progression.
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