数学与统计学院学术预告两则

报告题目1：Complex dynamics of a tumor-immune system with antigenicity

报 告 人：陈玉明教授

报告时间：2021年1月4日（周一）9:00—10:30

报告地点：腾讯会议ID: 301 176 685

报告摘要: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.

报告人简介:教授，博士生导师。主要研究兴趣为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，已在包括SIAM Journal on Mathematical Analysis、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 100 余篇，研究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4 项加拿大国家自然科学与工程理事会科研基金项目，参与3项中国国家自然科学基金面上项目。

报告题目2：HIV-1 model with infection age and drug-resistance

报 告 人： 刘胜强教授

报告时间：2021年1月4日（周一）10:30—12:00

报告地点：腾讯会议ID: 301 176 685

报告摘要:We propose a hybrid two-strain HIV dynamic model with mutation which describes the interactions of the healthy CD4+ T cells, infected CD4+ T cells and viruses, where two transmission modes, virus-to-cell and cell-to-cell, age structure and drug resistance are considered. We obtain the basic reproductive number for each strain. We conducted qualitative analyses of the model such as the asymptotic smoothness, uniform persistence and steady states stability. By subtle construction and estimates of Lyapunov functionals, we show that there exists the principle of competitive exclusion if there is no mutation, the disease-free and drug-resistant steady states are globally asymptotically stable if there is mutation. Furthermore, mutation, which from the drug-sensitive to drug-resistant strain, play a critical role in the existence and stability of steady states. Numerical simulations are also performed in order to illustrate the global dynamical behavior, and analyze the mutation impacts on dynamics of system.

报告人简介:天津工业大学教授，博士生导师。研究领域为生物数学、动力系统。先后主持国家自然科学基金3项，出版专著1本、参与编著两本，先后指导博士生10人，硕士生15人，在SIAM Journal on Applied Mathematics、Journal of Differential Equations、Journal of Nonlinear Science、Bulletin of Mathematical Biology、Mathematical Biosciences等应用数学领域知名学术期刊上发表SCI论文70余篇。

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