DYNAMIC MODELING AND ANALYSIS OF TUMOR ANGIOGENESIS AND ANTI-ANGIOGENESIS TREATMENT

Angiogenesis plays an important role in the development of tumor since it allows for the delivery of oxygen and nutrients. Understanding the dynamics of angiogenesis is essential for accurately characterizing tumor growth during the vascular phase and for developing models that optimize therapeutic strategies. In order to provide beneficial information and theoretical models for clinical research of tumor therapy strategies, a new mathematical model is established to describe the interaction between vascular epithelial cells and tumor cells. Through the stability analysis of the equilibria, the results show that in the absence of therapeutic intervention, the number of tumor cells will naturally stabilize at a positive value. Further, the anti-angiogenesis treatment term is added to the model to investigate the effects of anti-vascular therapy. The results indicate that anti-angiogenic therapy alone cannot completely eliminate a tumor, but can observably reduce the number of the tumor. Finally, numerical simulations are carried out to investigate the therapeutic effect of anti-vascular therapy combined with traditional treatment. The numerical simulation results show that the anti-angiogenesis therapy is a good adjunct to traditional therapy, which is beneficial to the design of better tumor treatment program.