報告題目:State-Structured Differential Equation Models for Infectious Diseases
報 告 人:Prof. Michael Y. Li 阿爾伯塔大學數學與統計學院
報告時間:5月16日 上午10:00-11:00
報告地點:數學樓一樓第一報告廳
報告摘要:
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.
報告人簡介:
李毅教授,1993年在加拿大阿爾伯塔大學獲得理學博士學位,1993-1995年先後在加拿大蒙特利爾大學和美國喬治亞理工學院做博士後,現任阿爾伯塔大學數學與統計學院教授。李毅教授主要研究領域為微分方程與動力系統、傳染病傳播建模和病毒動力學建模。他的研究先後得到了NSF(美國)、NSERC(加拿大)等多個基金資助。李毅老師緻力于将數學建模與公共衛生領域相結合,提出了著名的Li-Muldowney理論和李雅普諾夫函數的圖論方法證明傳染病數學模型的全局穩定性,并且領導了HIV抗逆轉錄病毒療法建模,估測未确診HIV陽性人群,結核病的傳播,預測流感季節和HIV在大腦中的傳播等多個跨學科項目。