报告时间：2025年5月15日下午14:00-16:00
报告地点：北区4号教学楼102室
报告题目：Dynamical analysis of a simple two-stage tumor-immune model、
报告摘要：In this talk, we propose a simple two-stage model on the interaction between tumor cells and lymphocytes. The model incorporates a linear function to represent the effect of tumor antigen stimulation and a logistic growth for tumors in the absence of immune response. We analyze the oscillatory behavior of tumor levels from three perspectives: the intrinsic growth rate, the killing rate of lymphocytes against tumor cells, and the stimulation effect of tumor antigens on the immune system. Theoretical analysis of Hopf bifurcation reveals the distinct differences among these factors. Oscillations occur between two critical values for the intrinsic growth rate and the killing rate of lymphocytes, while for the stimulation effect of tumor antigens, there is a single critical value that triggers the oscillation. Numerical simulations show that strong tumor antigen stimulation can induce long-term dormancy in tumor growth. Furthermore, we establish the equivalence between the local and global stability of the tumor-free equilibrium using the fluctuation lemma and derive a sufficient condition on the global attractivity of the tumor-present equilibrium by constructing auxiliary convergent sequences.
报告人简介：陈玉明，分别于1991年和1994年从北京大学获应用数学学士和硕士学位，2000年从加拿大约克大学获理学博士学位，2000年9月至2001年6月在加拿大阿尔伯塔大学做博士后，2001年7月起，任教于加拿大罗瑞尔大学，现为该校数学系正教授、博士生导师。主要研究动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。已在SIAM Journal on Mathematical Analysis, Transactions on the American Mathematical Society, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society，Mathematical Biosciences，Neural Networks等国际著名刊物发表论文一百九十余篇，其成果被同行广泛引用。曾获安大略省科技与创新部早期研究者奖。主持了6项加拿大国家自然科学与工程理事会科研基金项目，参与了3项中国国家自然科学基金面上项目，与中国学者有广泛交流与合作。
