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Related Experiment Video

Updated: Jun 28, 2026

Tumor Transplantation for Assessing the Dynamics of Tumor-Infiltrating CD8+ T Cells in Mice

Tumor Transplantation for Assessing the Dynamics of Tumor-Infiltrating CD8⁺ T Cells in Mice

Published on: June 12, 2021

Stochastic tumor immune dynamics with saturating response.

Javed Hussain¹, Tareq Saeed², Lianlian Zhou³

¹Department of Mathematics, Sukkur IBA University, Sukkur, Pakistan.

Scientific Reports

|June 26, 2026

Summary

This study models tumor-immune dynamics with random fluctuations, revealing that sustained immune pressure is crucial for tumor extinction. Persistence depends on a stochastic threshold influenced by interaction noise.

Keywords:

Empirical occupation measure Euler–Maruyama simulation.Invariant measure Persistence Positivity Saturating interaction Shared environmental noise Stochastic boundedness Stochastic tumor–immune model

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Area of Science:

Mathematical Biology
Immunology
Computational Science

Background:

Tumor-immune interactions are complex, involving dynamic population balances.
Stochastic models are essential for capturing random fluctuations in biological systems.

Purpose of the Study:

To analyze a stochastic tumor-immune interaction model with a saturating response.
To investigate the conditions for tumor extinction and population persistence.

Main Methods:

Stochastic differential equations with a single Brownian motion driving the interaction term.
Analysis of global positive solutions, population boundedness, and extinction criteria.
Application of Krylov-Bogoliubov averaging for invariant probability measures.

Main Results:

Unique global positive solutions exist for positive initial data.
Tumor extinction necessitates sustained immune pressure.
Persistence is governed by a stochastic threshold, with interaction noise creating an Itô correction.

Conclusions:

The model demonstrates that random fluctuations in immune contact influence tumor dynamics.
Sustained immune pressure is key for tumor eradication.
Numerical simulations support the model's predictions regarding persistence and saturation effects.