学术报告
报告题目：Talk 1: Chemotherapy with time-dependent infusion
Talk 2: Chemotherapy with time delay
报告人：韩晓莹 教授 （Auburn University, USA）
报告时间：2018年7月19日（星期四）下午14:30-17:00
报告地点：创新园大厦 A1101报告厅
校内联系人：柳振鑫 教授 联系电话：84708351-8039
报告摘要:
Abstract 1: Classical mathematical models for chemotherapy assume a constant infusion rate of the chemotherapy agent. However in reality the infusion rate usually varies with respect to time, due to the natural fluctuation of environments or clinical needs. In this work we study a non-autonomous chemotherapy model where the injection rate and injection concentration of the chemotherapy agent are time-dependent. In particular, we prove that the non-autonomous dynamical system generated by solutions to the non-autonomous chemotherapy system possesses a pullback attractor. In addition, we investigate the detailed interior structures of the pullback attractor to provide crucial information on the effectiveness of the treatment. The main analytical tool used is the theory of non-autonomous dynamical systems. Numerical experiments are carried out to supplement the analysis and illustrate the effectiveness of different types of infusions.
Abstract 2: A chemotherapy model for cancer treatment is studied, where the chemotherapy agent and cells are assumed to follow a predator-prey type relation. The time delays from the instant that the chemotherapy agent is injected to the instant that the treatment is effective are taken into account and dynamics of systems with or without delays are compared. First basic properties of solutions including existence and uniqueness, boundedness and positiveness are discussed. Then conditions on model parameters are established for different outcomes of the treatment. Numerical simulations are provided to illustrate theoretical results.
报告人简介：韩晓莹，美国奥本大学教授。主要从事随机和非自治动力系统的研究，也关注动力系统在生物、生态学中的建模、分析与模拟等。在数学专业重要杂志上发表学术论文30余篇，出版专著3部。
