报   告1. HIV model with cell-to-cell interaction and vectored immunoprohylasis experiment  

内容简介：We consider local and global bifurcations in a HIV model with both cell-to-cell interaction and vectored immunoprohylasis. Particular attention is focused on the effects due to the cell-to-cell transmission and the effect of the vectored immunoprohylasis. The backward bifurcation, Hopf bifurcation,  Bogdanov-Takens  bifurcation, isola bifurcation are investigated by using bifurcation theory and numerical simulations. It is shown that the effect of vectored immunoprohylasis is the main cause of the periodic symptoms in HIV disease. That is to say, vected immunoprohylasis is not always do benefit to the treatment of HIV, it may make the disease more complicated. Moreover, it is also shown that the increase of cell-to-cell interaction may be the main factor causing Hopf bifurcation to disappear, and thus eliminating oscillation behaviour. Also, different patterns of dynamical behaviors are found including the bistable phenomenon.

报  告2. Global dynamics of avian influenza with nonlinear recovery rate and psychological effect

内容简介：In this paper, we construct an SI-SEIR type avian influenza epidemic model with psychological effect and nonlinear recovery rate to study the roles of saturation inhibition effect, psychological effect and available resources of public health systems (especially the number of hospital beds) on the transmission and control of avian virus. Through setting the basic reproductive number as the threshold parameter and constructing Liapunov function, Dulac function and the second additive compound matrix to prove the global stability of disease-free equilibria and endemic equilibrium. Theoretical analysis results show that the saturation inhibition effect, psychological effect and effective medical resources could reduce the peak value and the final number of infected population.

报    告3. Modeling the population dynamics of Empoasca vitis Gothe with tea-leaves

内容简介:In this paper, a new four-dimensional stage-structured model about the famous Longjing Tea and the Empoasca vitis Gothe are built by considering three stages: eggs, numphs and adults E. vitis, which can help us to know about the relationships between the tea leaves and pests.  Local and global stability of equilibria with all parameters are investigated.  Finally, the results are also verified by numerical simulations.

报告人：徐衍聪  教授

报告时间： 2019年4月21日8:30-11:30

报告地点：002cc白菜资讯三楼报告厅

徐衍聪教授简介：杭州师范大学教授,硕士生导师,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, Nonlinear Wave,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项目及参与各类基金10余项。