[MS13] Mathematical Modeling and Computing in Epidemiology

[MS13-01] Bifurcation Analysis in a Tumor-Immune System Interaction Model

*Yasuhiro Takeuchi¹ (1. Aoyama Gakuin University (Japan))

Keywords:

tumor-immune system,immune response delay,Hopf bifurcation,BT bifurcation

We study a tumor-immune system interaction model with dendritic cell therapy and immune response delay. Our results reveal that the delay can destabilize the stable positive equilibrium through Hopf bifurcation. Furthermore, the direction and stability of Hopf bifurcation are derived. When there is a cusp, we show that it is a BT singularity for any delay and the delay model also undergoes BT bifurcation. Finally, numerical simulations are presented to illustrate the theoretical results.