Modeling, Analysis, and Optimal Control of Leukemic Cell Population Dynamics Under Therapy

Area of Science:

• Mathematical Biology
• Computational Oncology
• Systems Biology

Background:

• Existing ordinary differential equation (ODE) models describe healthy and leukemic cell dynamics.
• Chemotherapy's impact on these dynamics requires a more refined mathematical framework.

Purpose of the Study:

• To extend an existing ODE model by incorporating a chemotherapy control variable.
• To establish a mathematical basis for investigating anti-cancer strategies.
• To optimize chemotherapy regimens for minimizing leukemia stem cells and drug toxicity.

Main Methods:

• Stability analysis of system equilibria using clinical data.
• Optimal control problem formulation using Pontryagin's Maximum Principle.
• Direct numerical optimization and sensitivity analysis.

Main Results:

• Identification of a complex equilibrium structure, including a continuum of coexistence states and bifurcation thresholds.
• Demonstration of a turnpike phenomenon where dynamic trajectories approach ideal static structures over time.
• Sensitivity analysis providing insights into biological mechanisms influencing optimal therapeutic outcomes.

Conclusions:

• The extended framework offers a refined mathematical basis for anti-cancer strategy investigation.
• The study highlights unconventional features in optimal control problems due to complex equilibria.
• Findings suggest potential for improved chemotherapy optimization based on identified biological mechanisms.