*主持人：刘兴波 教授

*讲座内容简介：

In this paper, the nonlinear dynamics of a SIRS epidemic model with vertical transmission rate of neonates, nonlinear incidence rate and nonlinear recovery rate are investigated. We focus on the influence of public available resources (especially the number of hospital beds) on disease control and transmission. The existence and stability of equilibria are analyzed with the basic reproduction number as the threshold value. The coexistence of limit cycle and homoclinic cycle, and the coexistence of stable limit cycle and unstable limit cycle are also obtained. This study indicates that maintaining enough number of hospital beds is very crucial to the control of the infectious diseases no matter whether the immunity loss population are involved or not.

*主讲人简介：

徐衍聪教授，华东师范大学应用数学博士，浙江大学博士后，杭州师范大学数学系教授，博士生导师，美国（SIAM）工业与应用数学会员，美国数学评论评论员。先后访问美国布朗大学、日本京都大学、德国不莱梅大学,加拿大约克大学等高校。目前主要从事动力系统分支理论、局部结构分支及应用研究，主要包括：Dynamical Systems, Dynamics of Patterns，Homoclinic and Heteroclinic Phenomena等研究工作。主持国家自然科学基金面上项目、浙江省自然科学基金，日本GCOE项目等各类基金10余项。