应数学与统计学院邀请，日本青山学院大学（Aoyama Gakuin University）数学与物理系教授Yasuhiro TAKEUCHI于9月3日-10日来我校进行学术交流并作系列学术报告。

题 目：Mathematical Modelling of Tumor Immune System Interaction

时 间：2017年9月8日（周五）， 上午9：00～11：00

地 点：理科楼408会议室

摘 要： We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays, namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs). By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter. Our results exhibit that both delays do not affect the stability of tumor-free equilibrium. However, they are able to destabilize the immune-control equilibrium and cause periodic solutions. We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors. The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium. Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.

报告人简介：Yasuhiro TAKEUCHI教授在日本京都大学获得博士学位。主要从事生物数学和传染病动力学领域的研究，尤其是时滞微分方程理论及其在生态系统和传染病中的应用研究。Yasuhiro TAKEUCHI教授曾担任日本生物数学会主席，目前担任国际杂志《Mathematical Biosciences and Engineering》和《Japan Journal of Industrial and Applied Mathematics》的副主编，同时也是《Journal of Theoretical Biology》、《Journal of Biological Dynamics》等杂志的编委。出版了专著8部，已经在《SIAM Journal on Applied Mathematics》、《Journal of Theoretical Biology》、《Bulletin of Mathematical Biology》、《Journal of Mathematical Biology》、《PLoS ONE》、《Mathematical Biosciences》等国际权威期刊上发表学术论文170多篇。主持日本自然科学基金项目10多项。

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