理學院數學系學術報告--Michael Y. Li教授學術講座
[ 作者:李文學 來源:理學院 瀏覽:10 錄入時間:2019年05月16日 ]


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

(二)Modeling HIV/SIV Infections in Brain


    應理學院數學系邀請,加拿大阿爾伯塔大學(University of Alberta)李毅(Michael Y. Li)教授將于20190522日至0525日訪問我校數學系,期間將作兩場學術報告,歡迎感興趣的師生參加。






(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.



    李毅(Michael Y. Li)教授,加拿大阿爾伯塔大學教授兼阿爾伯塔大學應用數學研究所所長。本科和碩士研究生學業是在吉林大學數學專業完成的,其于1987年赴加拿大阿爾伯塔大學留學,于1993年獲得博士學位。之后獲得了加拿大Montreal大學和美國Georgia工業大學博士后,并于2004年成為阿爾伯塔大學正教授。2007年受聘擔任哈工大境外兼職博導。Michael Y. Li 教授是北美地區在微分方程與動力系統及應用的研究領域中最活躍的學者之一。他和Muldowney以復合陣理論為基礎,建立的高維常微分方程定性理論對常微分方程和時滯微分方程的研究產生了巨大影響。許多學者把他們的理論應用于某些有實際背景的高維常微分方程的全局穩定性及某些時滯微分方程的周期解的全局存在性的研究中,得到了非常好的結果。Michael Y. Li教授共發表高水平數學雜志論文70余篇,大多是數學專業頂級期刊,包括 SIAM J. Math. Anal.,SIAM J. Appl. Mathbbin赌博网,J. Differ. Equ.bbin赌博网,JMB, J. Math. Anal. Appl.等。其中,發表在J. Differ. Equ.上的高被引論文“Global-stability problem for coupled systems of differential equations on networks”文章被引次數已達283次,為微分方程領域做出了杰出的貢獻。目前,他的研究興趣包括非線性微分方程和動力學系統,生物學、流行病學和醫學中的數學建模等。