学术讲座【Modelling and Analysis of Recurrent Infections】

时间：2014年12月18日（星期四）下午4:00-5:00

地点：仓山校区成功楼603报告厅

主讲：加拿大西安大略大学 郁培教授、博士生导师

主办：数学与计算机科学学院

专家简介：郁培，加拿大西安大略大学应用数学系教授、博士生导师，常微分方程与动力系统领域著名专家，在微分方程定性、分支理论等研究领域做出了杰出的工作，已在《SIAM Review》等期刊发表系列论文以及Springer等出版社出版了多部专著，其中《Normal forms, Melnikov functions and bifurcation of limit cycles》（与韩茂安教授合作）被列为《Applied Mathematical Sciences》第181册（2012年出版）。现任《Journal of Applied Analysis and Computation》、《International Journal of Bifurcation and Chaos》与《Communications in Nonlinear Science and Numerical Simulation》编委。

报告摘要： In this talk, we will present dynamic models of recurrent infections in individuals. These viral infections, HIV being a well-known example, have long periods of low viral activity punctuated by episodes of high viral reproduction. Previous models of the dynamics of these viral blips used either stochastic components or forcing terms as the triggers to simulate the phenomenon. The new developed models require neither stochastic features nor forcing terms and generate the viral blips by dynamic bifurcations. Using dynamical systems theory, we hypothesize four conditions for the existence of viral blips in a deterministic in-host infection model. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. Other possible mechanisms of generating blips will also be discussed.