Complex dynamics of a tumor-immune system with antigenicity

讲座时间 Datetime: 2022年6月18日，星期六， 21:00-22:30

地点 Venue: 腾讯线上会议：955979459

 主持人 Host：唐德

报告人 Speaker:陈玉明 

单位 Affiliation:加拿大罗瑞尔大学

报告摘要 Abstract:

Taking into account the effect of antigenicity, we propose and analyze a conceptual model for the tumor-immune interaction. The model is described by a system of two ordinary differential equations. Though simple, the model can have complicated dynamical behaviors. Besides the tumor-free equilibrium, there can be at most three tumor-present equilibria. The tumor-present equilibrium can be a saddle or stable node/focus. Sufficient conditions on the nonexistence of nonconstant periodic solutions are provided. Bifurcation analysis including Hopf bifurcation and Bogdanov-Takens bifurcation is carried out. The theoretical results are supported by numerical simulations. Numerical simulations reveal the complexity of the dynamical behaviors of the model, which includes the subcritical/supercritical Hopf bifurcation, homoclinic bifurcation, saddle-node bifurcation at a nonhyperbolic periodic orbit, the appearance of two limit cycles with a singular closed orbit, and so on. Some biological implications of the theoretical results and numerical simulations are also provided.