学术报告

题      目：Spatiotemporal Dynamics in Epidemic Models with Levy Flights: A Fractional Diffusion Approach

报  告  人：阮士贵  教授  (邀请人：丁维维 )

                                    美国迈阿密大学数学系

时      间：12月15日  10：00-11：00

地     点：数科院东楼401

报告人简介:

        阮士贵，美国迈阿密大学数学系教授。1992年获得加拿大阿尔伯特(Alberta)大学数学系博士学位，1992-1994年在加拿大菲尔兹数学所(Fields Institute)和麦克马斯特(McMaster)大学做博士后。1994-2002年在加拿大道尔豪斯(Dalhousie)大学数学与统计系先后任助理教授和副教授。现为美国迈阿密大学(University of Miami)数学系终身教授。主要研究领域是动力系统和微分方程及其在生物和医学中的应用，在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》等学术期刊上发表了约200篇学术论文，受到了国内外同行的关注与大量引用，2014和2015年连续被汤森路透集团列为全球高被引科学家。担任了一些重要学术期刊如《BMC Infectious Diseases》、《Bulletin of Mathematical Biology》、《DCDS-B》、《Mathematical Biosciences》等的编委，是《Mathematical Biosciences and Engineering》的主编（数学）。作为项目负责人多次获得美国国家卫生研究院（NIH）、美国国家科学基金（NSF）等资助。2013年获得海外及港澳学者合作研究基金资助。

摘      要：

        Recent field and experimental studies show that mobility patterns for humans exhibit scale-free nonlocal dynamics with heavy-tailed distributions characterized by Levy flights. To study the long-range geographical spread of infectious diseases, in this paper we propose a susceptible-infectious-susceptible epidemic model with Levy flights in which the dispersal of susceptible and infectious individuals follows a heavy-tailed jump distribution. Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. The primary focuses are on the existence and stability of disease-free and endemic equilibria and the impact of dispersal rate and fractional power on spatial profiles of these equilibria. A variational characterization of the basic reproduction number R0 is obtained and its dependence on the dispersal rate and fractional power is also examined. Then R0 is utilized to investigate the effects of spatial heterogeneity on the transmission dynamics. It is shown that R0 serves as a threshold for determining the existence and nonexistence of an epidemic equilibrium as well as the stabilities of the disease-free and endemic equilibria. In particular, for low-risk regions, both the dispersal rate and fractional power play a critical role and are capable of altering the threshold value. Numerical simulations were performed to illustrate the theoretical results. (Based on G. Zhao & S. Ruan, J. Math Pures Appl. 2023).

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