Effect of treatment on the global dynamics of delayed pathological angiogenesis models

Area of Science:

• Mathematical biology
• Oncology
• Pharmacology

Background:

• Angiogenesis plays a crucial role in tumor growth and metastasis.
• Therapeutic strategies often target tumor cells and the process of angiogenesis.
• Mathematical models are essential for understanding complex biological systems like cancer progression.

Purpose of the Study:

• To investigate the efficacy of continuous and impulse therapies in suppressing tumor growth and angiogenesis.
• To analyze mathematical models of angiogenesis with variable delays.
• To establish conditions for the global stability of cancer-free solutions.

Main Methods:

• Development and analysis of mathematical models for angiogenesis with variable delays.
• Application of continuous and impulse control strategies.
• Derivation of explicit conditions for global stability.
• Estimation of decay rates for tumor volume and pathological angiogenesis.

Main Results:

• Explicit conditions for the global stability of the cancer-free solution were derived for both continuous and impulsive therapy models.
• Delay-dependent estimates for the decay rates of tumor volume were obtained.
• Delay-dependent estimates for the decay rates of pathological angiogenesis were obtained.

Conclusions:

• Continuous and impulse therapies can effectively suppress tumor growth and angiogenesis.
• The stability and decay rates are dependent on the model's delay parameters.
• Mathematical modeling provides valuable insights into optimizing anti-cancer therapeutic strategies.