Dynamics and bifurcation of a hybrid competition model with applications to adaptive cancer therapy

Area of Science:

• Mathematical Oncology
• Cancer Therapeutics
• Computational Biology

Background:

• Adaptive therapy is a cancer treatment strategy that exploits competition between drug-sensitive and resistant cells to overcome drug resistance.
• The mathematical underpinnings of adaptive therapy are not fully understood, creating challenges in optimizing intervention timing and intensity.

Purpose of the Study:

• To develop and analyze a mathematical model for adaptive therapy incorporating periodic tumor monitoring and threshold-based interventions.
• To investigate the existence and stability of periodic solutions within the proposed model.
• To explore the impact of key parameters, such as threshold value and monitoring period, on treatment outcomes.

Main Methods:

• Development of a competition model for tumor growth with drug-sensitive and resistant cell populations.
• Application of bifurcation theory to analyze the existence and stability of periodic solutions.
• Numerical simulations to study parameter dependencies and treatment failure dynamics.

Main Results:

• Demonstration of novel (ℓ, m)T boundary periodic solutions and analysis of their stability.
• Proof of the existence and stability of positive periodic solutions using bifurcation theory.
• Numerical findings indicate that time to treatment failure depends non-linearly on the killing rate of sensitive cells, with a plateau effect.

Conclusions:

• Maximizing the killing rate of sensitive cells does not guarantee optimal therapeutic outcomes in adaptive therapy.
• Implementing a threshold value for interventions can extend patient survival time.
• Threshold-based adaptive therapy shows therapeutic benefit for tumor control by managing cell population dynamics.