报告题目：State-Structured Differential Equation Models for Infectious Diseases

报 告 人：Prof. Michael Y. Li 阿尔伯塔大学数学与统计学院

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 for infectious diseases.

The state is a measure of infectivity of an infected individual in epidemic models or the

intensity of viral replications in an infected cell for in-host models. In modelling,

a state structure can be either discrete or continuous.

In a discrete state structure, a model is described by a large system of coupled

ordinary differential equations (ODEs). The complexity of the system often poses a

serious challenge for the analysis of system dynamics. I will show how such a complex

system can be viewed as a dynamical system defined on a transmission-transfer

network (digraph), and how a graph-theoretic approach to Lyapunov functions

developed by Guo-Li-Shuai can be applied to rigorously establish the global dynamics.

In a continuous state structure, the model gives rise to a system of nonlinear

integro-differential equations with a nonlocal term. The mathematical challenges

for such a system include a lack of compactness of the associated nonlinear semigroup.

The well-posedness and dissipativity of the semigroup is established by directly verifying

the asymptotic smoothness. An equivalent principal spectral condition between the

next-generation operator and the linearized operator allows us to link the basic

reproduction number R0 to a threshold condition for the stability of the disease-free

equilibrium. The proof of the global stability of the endemic equilibrium utilizes a

Lyapunov function whose construction is informed by the graph-theoretic

approach in the discrete case.

报告人简介：

李毅教授，1993年在加拿大阿尔伯塔大学获得理学博士学位，1993-1995年先后在加拿大蒙特利尔大学和美国乔治亚理工学院做博士后，现任阿尔伯塔大学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。