学术报告报告主题: Spatiotemporal Dynamics in Epidemic Models with Levy Flights: A Fractional Diffusion Approach
报告人: 阮士贵 教授
报告时间：2023年12月13日（星期三）上午10:00-11:00
报告地点：四号楼4318
邀请人：刘锐 教授
欢迎广大师生前往！
数学学院
2023年12月13日
报告摘要：
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.
报告人介绍：
美国迈阿密大学数学系教授。主要学术成就包括白血病的数学建模和分析、非典（SARS）传播的建模与控制、人类免疫缺陷病毒I型（HIV—I）的感染动力学研究、媒介传播（Vector—borne）疾病的建模与理论分析、生态与传染病模型的多参数分支分析、浮游生物系统的动力学等。