报告题目：State-StructuredDifferential Equation Models for Infectious Diseases

报告人：Prof. Michael Y. Li阿尔伯塔尊龙凯时数学与统计学院

报告时间：5月16日上午10:00-11:00

报告地点：数学楼一楼第一报告厅

报告摘要：

In this talk, I will first introduce the concept of state structures forinfectious diseases.The state is a measure ofinfectivity of an infected individual in epidemic models or theintensity of viral replications inan infected cell for in-host models. In modelling,a state structure can be eitherdiscrete or continuous.

In a discrete state structure, a model is described by a large system of coupledordinary differential equations(ODEs). The complexity of the system often poses aserious challenge for the analysisof system dynamics. I will show how such a complexsystem can be viewed as a dynamicalsystem defined on a transmission-transfernetwork (digraph), and how agraph-theoretic approach to Lyapunov functionsdeveloped by Guo-Li-Shuai can beapplied to rigorously establish the global dynamics.

In a continuous state structure, the model gives rise to a system of nonlinearintegro-differential equations witha nonlocal term. The mathematical challengesfor such a system include a lack ofcompactness of the associated nonlinear semigroup.The well-posedness anddissipativity of the semigroup is established by directly verifyingthe asymptotic smoothness. Anequivalent principal spectral condition between thenext-generation operator and thelinearized operator allows us to link the basicreproduction number R0 to athreshold condition for the stability of the disease-freeequilibrium. The proof of theglobal stability of the endemic equilibrium utilizes aLyapunov function whoseconstruction is informed by the graph-theoreticapproach in the discrete case.

报告人简介：

李毅教授，1993年在加拿大阿尔伯塔尊龙凯时获得理学博士学位，1993-1995年先后在加拿大蒙特利尔尊龙凯时和美国乔治亚理工学院做博士后，现任阿尔伯塔尊龙凯时数学与统计学院教授。李毅教授主要研究领域为微分方程与动力系统、传染病传播建模和病毒动力学建模。他的研究先后得到了NSF（美国）、NSERC（加拿大）等多个基金资助。李毅老师致力于将数学建模与公共卫生领域相结合，提出了著名的Li-Muldowney理论和李雅普诺夫函数的图论方法证明传染病数学模型的全局稳定性，并且领导了HIV抗逆转录病毒疗法建模，估测未确诊HIV阳性人群，结核病的传播，预测流感季节和HIV在大脑中的传播等多个跨学科项目。