Noise-Driven Tipping in a Tumor-Immune Model with Optimal Combination Therapy

Area of Science:

• Mathematical Oncology
• Computational Biology
• Immunology

Background:

• Tumor-immune interactions are complex and unpredictable, contributing to high cancer mortality.
• Tumor progression can exhibit multistability, making it difficult to anticipate malignant changes.

Purpose of the Study:

• To develop and analyze a mathematical model of tumor-immune dynamics incorporating chemotherapy.
• To investigate how chemotherapy-induced toxicity influences tumor states and progression.
• To explore the role of stochasticity and develop early-warning signals for cancer progression.

Main Methods:

• Deterministic analysis and continuation of a novel tumor-immune model.
• Stochastic analysis incorporating environmental and demographic noise.
• Development and assessment of early-warning indicators for state transitions.
• Formulation of an optimal control problem for combination therapy.

Main Results:

• Chemotherapy-induced toxicity can create hysteresis and bistability between tumor dormancy and uncontrolled growth.
• Both environmental and demographic stochasticity can induce switching between tumor states.
• Demographic noise enhances tumor resilience, while environmental noise may suppress growth.
• Early-warning signals can predict transitions from dormancy to full growth, with composite measures being more robust.
• Optimized combination therapy can significantly reduce tumor burden from either dormancy or full-growth states.

Conclusions:

• Mathematical modeling provides insights into unpredictable cancer progression and treatment responses.
• Chemotherapy can alter tumor dynamics, potentially leading to abrupt progression.
• Stochasticity plays a crucial role in tumor fate, influencing resilience and growth.
• Early detection of critical transitions and tailored interventions are vital for preventing catastrophic tumor progression.