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理学院数学系学术报告--Michael Y. Li教授学术讲座
[ 作者:李文学 来源:理学院 浏览:30 录入时间:2019年05月16日 ]

理学院数学系学术报告:

(一)Mathematical Models for Infectious Diseases with Nonlocal State Structures

(二)Modeling HIV/SIV Infections in Brain

 

    应理学院数学系邀请,加拿大阿尔伯塔大学(University of Alberta)李毅(Michael Y. Li)教授将于20190522日至0525日访问我校数学系,期间将作两场学术报告,欢迎感兴趣的师生参加。

 

报告时间:第一场,20190523日,时间,8:30-9:30

 第二场,20190524日,时间,10:00-11:00

报告地点:H203

报告题目

(一)Mathematical Models for Infectious Diseases with Nonlocal State Structures

Abstract In this talk, I will introduce state structures in mathematical models 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.

(二)  Modeling HIV/SIV Infections in Brain

Abstract: Understanding HIV-1 replication and latency in different reservoirs is an ongoing challenge in the care of patients with HIV/AIDS. A mathematical model was created to describe and predict the viral dynamics of HIV-1 and SIV infection within the brain during effective combination antiretroviral therapy (cART). We combine the available clinical data and the mathematical model to provide insight on the dynamics of the HIV infection in brain and discuss the effectiveness of the "shock-and-kill" strategy of eliminating HIV/SIV from the body.

 

主讲人简介:

    李毅(Michael Y. Li)教授,加拿大阿尔伯塔大学教授兼阿尔伯塔大学应用数学研究所所长。本科和硕士研究生学业是在吉林大学数学专业完成的,其于1987年赴加拿大阿尔伯塔大学留学,于1993年获得博士学位。之后获得了加拿大Montreal大学和美国Georgia工业大学博士后,并于2004年成为阿尔伯塔大学正教授。2007年受聘担任哈工大境外兼职博导。Michael Y. Li 教授是北美地区在微分方程与动力系统及应用的研究领域中最活跃的学者之一。他和Muldowney以复合阵理论为基础,建立的高维常微分方程定性理论对常微分方程和时滞微分方程的研究产生了巨大影响。许多学者把他们的理论应用于某些有实际背景的高维常微分方程的全局稳定性及某些时滞微分方程的周期解的全局存在性的研究中,得到了非常好的结果。Michael Y. Li教授共发表高水平数学杂志论文70余篇,大多是数学专业顶级期刊,包括 SIAM J. Math. Anal.SIAM J. Appl. MathJ. Differ. Equ.JMB J. Math. Anal. Appl.等。其中,发表在J. Differ. Equ.上的高被引论文“Global-stability problem for coupled systems of differential equations on networks”文章被引次数已达283次,为微分方程领域做出了杰出的贡献。目前,他的研究兴趣包括非线性微分方程和动力学系统,生物学、流行病学和医学中的数学建模等。

 


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