讲座内容简介：The global stability of equilibria of epidemic models plays an important role in understanding the underlying disease transmission mechanisms. One of the most powerful approaches to determine global stability is Lyapunov's direct method. The method involves constructing an appropriate Lyapunov function and verifying negative (semi-)definiteness of its derivative along solutions, which often are not easy to achieve. This talk reports some new ideas on applying Lyapunov's direct method. On the one hand, a new kind of function for constructing Lyapunov functions is given. On the other hand, a new procedure to determine whether a given Lyapunov function candidate works or not is developed. The procedure consists of a novel way to rearrange the terms of the derivative along solutions.

讲座人简介：陈玉明教授，分别于1991年和1994年从北京大学获应用数学学士学位和硕士学位，并于2000年从加拿大约克大学（York University）获理学博士学位。从2001年至今，一直任教于加拿大罗瑞尔大学(Wilfrid Laurier University)。现为该校数学系教授、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, 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百余篇，曾获安大略省科技与创新部早期研究者奖。主持了4项加拿大国家自然科学与工程理事会(NSERC)科研基金项目。