Academic Report
Title: Talk1: Chemotherapy with time-dependent infusion
Talk 2:Chemotherapy with time delay
Reporter: Prof. HAN Xiaoying (Auburn University, USA)
Time: July 19, 2018 (Thursday) PM 14:30-17:00
Location:A1101# room, Innovation Park Building
Contact: Prof. LIU Zhenxin (tel: 84708351-8039)
Abstract: 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.
The brief introduction to the reporter: Han Xiaoying, a professor at Auburn University in the United States, is mainly engaged in the research of random and non autonomous dynamic systems, and also focuses on modeling, analysis and Simulation of power systems in biology and ecology. She has published more than 30 academic papers and 3 monograph in the major journals of mathematics.
