报告人：Prof.Shigui Ruan （Department of Mathematics，University of Miami，华东师范大学客座教授）
报告I：Bifurcations in Biological Models
时间：2009年1月5日（星期二）上午10：00-11:00
地点：数学楼102报告厅
摘要：Since many biological phenomena can be modeled by a set of differential equations according to certain idealized physical laws, it is very important to understand the dynamics of these equations in order to understand the biological phenomena. The physical laws are modeled in terms of parameters, so it is crucial to determine how many parameters and how these parameters affect the dynamics of the system. There are many interesting and challenging bifurcation problems in biological models, such as homoclinic bifurcations and chaos in epidemic models, higher codimension (2, 3 or 4) bifurcations in predator-prey models, Bogdanov-Takens bifurcation in delayed biological models, etc. In this talk I will introduce some bifurcation problems arise from studying various biological and epidemiological models.

报告II：Mathematical Modeling of Some Infectious Diseases
时间：2009年1月9日（星期五）下午1：30-2:30
地点：数学楼102报告厅
摘要：The spread of many infectious diseases can be modeled by mathematical equations according to certain idealized physical laws. The physical laws are described in terms of parameters. The basic reproduction number (R0) is an important concept in studying the transmission and control of infectious diseases which is defined as the expected average number of secondary cases produced by an index case during its infectiousness period. Roughly speaking, a disease can be controlled or even can die out if R0<1; it spreads out or becomes endemic if R0>1. Mathematical modeling and analysis plays a crucial role in evaluating R0 in terms of model parameters and understanding the spread of the diseases. In this talk, we will introduce some basic epidemic models and some recent work on modeling malaria, transmission of antibiotic-resistant bacteria in hospital and some other diseases.