Reaction-diffusion modeling of vascular tumor growth: Bifurcation, relapse, and therapy efficacy

The vascular tumor growth model proposed by Pinho et al. has gained attention in studies of the effect of anti-angiogenic therapy. In the present work, we extend Pinho's model to a reaction-diffusion model with different cell growth behaviors to evaluate the individual and combined effects of chemotherapy, anti-angiogenic therapy, and immunotherapy across different stages of vascular cancer. Analysis of the model includes the existence and stability of up to six different equilibria with bifurcations that define the transitions between them. By establishing conditions for the stability of the cancer-free equilibrium, we numerically explore different dynamics of cancer relapse. This includes examining the timing and frequency of relapse and identifying thresholds for critical treatment parameters. Furthermore, the numerical simulations of the extended model show that in the advanced stages of cancer, the integration of chemotherapy, immunotherapy, and anti-angiogenic therapy is essential for effective control of vascular cancer and reduces the overall duration of treatment.