Dynamical analysis of an impulsive model of cancer cell populations under radiotherapy

Area of Science:

• Mathematical Oncology
• Biomedical Engineering
• Differential Equations

Background:

• Cancer treatment efficacy depends on understanding tumor growth dynamics.
• Radiation therapy (RT) is a key cancer treatment modality.
• Mathematical models are crucial for analyzing treatment outcomes.

Purpose of the Study:

• To analyze an impulsive differential equation model for cancer treatment using RT.
• To investigate the conditions for cancer cell persistence and eradication.
• To explore the stability of periodic solutions in cancer treatment models.

Main Methods:

• Development of an impulsive differential equation model for RT.
• Analytical investigation of cancer cell volume dynamics.
• Analysis of periodic solutions and their stability.
• Modification of the model to enhance RT effectiveness.
• Numerical simulations for result validation.

Main Results:

• The initial model showed that periodic solutions, if they exist, are unstable.
• A modified model demonstrated conditions for a globally stable periodic solution.
• The modified model suggests the possibility of periodic tumor regression.
• Analytical results illuminate the interplay between tumor growth and RT.

Conclusions:

• The stability of periodic solutions is critical for predicting treatment outcomes.
• A modified RT model offers a more optimistic outlook with potential for stable regression.
• Mathematical modeling provides valuable insights into optimizing cancer treatment strategies.