Bifurcation Analysis of Mathematical Model of Prostate Cancer with Immunotherapy

Abstract

Immunotherapy using dendritic cells (DCs) as antigen-presenting cells is widely used in laboratory and animal studies as a promising treatment for advanced prostate cancer. In this paper, the bifurcation analysis of a nonlinear model of prostate cancer with immunotherapy is performed. It is found that the model exhibits complex behaviors such as a saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and generalized Hopf bifurcation. Moreover, it is shown that the vaccine amount and T-cells killing efficiency of tumor cells have a significant effect on tumor cells, which provides new insights to improve treatment outcomes even for patients with a weak immune system.