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

報(bào)告人：Shigui Ruan, University of Miami, USA

時(shí)間:  10月17日（周二）下午15: 30-16: 20

地點(diǎn)：30456

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).

個(gè)人簡(jiǎn)介：阮士貴，1983年本科畢業(yè)于華中師范大學(xué)數(shù)學(xué)系，1988年獲得華中師范大學(xué)數(shù)學(xué)系碩士學(xué)位，1992年獲得加拿大阿爾伯塔大學(xué)數(shù)學(xué)系博士學(xué)位，1992-1994年在加拿大菲爾茲數(shù)學(xué)所和麥克馬斯特大學(xué)做博士后。1994-2002年在加拿大道爾豪斯大學(xué)數(shù)學(xué)與統(tǒng)計(jì)系先后任助理教授和副教授，現(xiàn)為美國(guó)邁阿密大學(xué)數(shù)學(xué)系終身教授。主要研究領(lǐng)域是動(dòng)力系統(tǒng)和微分方程及其在生物和醫(yī)學(xué)中的應(yīng)用。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《Trans Amer Math Soc》、《J Funct Anal》、《Math Ann》、《J Math Pures Appl》等學(xué)術(shù)期刊上發(fā)表了200多篇學(xué)術(shù)論文，受到了國(guó)內(nèi)外同行的關(guān)注與大量引用，2014 和2015 年連續(xù)被湯森路透集團(tuán)列為全球高被引科學(xué)家。擔(dān)任了一些重要學(xué)術(shù)期刊如《Bulletin of Mathematical Biology》（高級(jí)編委）、《Journal of Mathematical Biology》、《Mathematical Biosciences》等的編委，是《Mathematical Biosciences and Engineering》的主編（數(shù)學(xué)）。作為項(xiàng)目負(fù)責(zé)人多次獲得美國(guó)國(guó)家衛(wèi)生研究院（NIH）、美國(guó)國(guó)家科學(xué)基金（NSF）、國(guó)家自然科學(xué)基金會(huì)資助。2013年獲得海外及港澳學(xué)者合作研究基金（原海外杰青）資助。

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