数学一级学科Seminar 681
题目： 两斑图间流行性病毒的传播、扩散以及Allee效应
报告人：宋宝军 副教授(Montclair State University, USA)
时间：2013年5月8日（周三)15:30
地点：校本部G507
主办部门：理学院数学系

摘要：

        We first explore the population dynamics of predator-prey systems when their interactions are mediated by a prey population with access to a refuge. The emphasis is in situations when differences in prey abundance in refuge and non-refuge habitats are the drivers of prey dispersal. It is shown that as dispersal increases, the system experiences transitions from predator-prey extinction, to predator-prey oscillatory stable co-existence, to predator prey stable non-oscillatory co-existence with the outcomes depending on initial conditions. If the Allee effect is applied to prey populations, bifurcation approaches, asymptotic analysis and numerical imulations are extensively used to discuss the possibility of bi-stability, tri-stability and  up to 6-stability all leading to distinct outcomes. As a result, the interactions among dispersal, a refuge and the Allee effect together can increase the type of dynamics. Furthermore, whenever randomness is an important force in the invasion process of a habitat (initial conditions) then one would expect, in the presence of dispersal corridors, the coexistence of identical predator-prey system that exhibit dramatically different population patterns. 

        Then, patch models are also constructed and analyzed to study the role of a migratory bird population in the transmission of the highly pathogenic H5N1 strain of avian influenza. Our discrete models consider a  igratory bird population and two local bird populations. The local bird populations live in their own patches and the migratory birds migrate back and forth between patches seasonally. The models are tested by using the prevalence of avian influenza in Mallard Duck by season in United States and Canada from 1974 to 1986. Both our analytic results and simulations predict a pattern of seasonal oscillation of the prevalence of avian influenza in Mallard Duck A variety types of demographic growth modes are discussed. The models for most nonlinear reproductions or nonlinear survive functions undergo double period-double bifurcations.