Spatial Segregation in Reaction-Diffusion Epidemic Models

主讲人：王皓 加拿大阿尔伯塔大学终身教授

时间：2022年11月12日10：00

地点：腾讯会议 478 127 447

举办单位：数理学院

主讲人介绍：王皓，现为加拿大阿尔伯塔大学终身教授，数学生态学与流行病学交叉实验室（ILMEE）主任。他在化学计量和认知运动理论及其在生物降解、生态毒理学和传染病中的应用等领域取得了许多重要研究成果，发表SCI论文百余篇，其中大部分成果发表在 SIAM J. Appl. Math., JDE, JMB, Nonlinearity, J Nonlinear Sci等国际著名期刊。目前领导着一个由30名博士后和研究生组成的科研团队，获得了多项NSERC基金资助。他培养了很多优秀的博士生和博士后，其中部分已经成为加拿大、美国、中国和韩国等地的教授，以及一些顶尖大学的博士后。由于出色的指导博士生和博士后的经历，他获得了FGSR优秀导师奖和约瑟芬·米切尔优秀指导奖。由于出色的研究工作，他获得了NSERC个人探索奖和一些优秀科研职业奖。他目前担任《Mathematical Biosciences and Engineering》的主编、《Journal of Mathematical Biology》、《Bulletin of Mathematical Biology》、《Mathematical Biosciences》和DCDS-B的编委，以及《Nonlinear Dynamics and Systems Theory》的北美主编。

内容介绍：I will present SIS reaction-diffusion epidemic models with cognition and show the impact of movement strategies on disease outbreak and mitigation under a spatially heterogeneous environment. The cognitive diffusion either takes a Fokker-Planck type diffusion obtained by Chapman's diffusion law (called random diffusion) or follows Fick's diffusion law (called symmetric diffusion). We derive a variational expression of the basic reproduction number R0 for both models and prove that the disease-free equilibrium is unique and globally asymptotically stable if R0<1. Furthermore, if R0>1, the model following Fick's diffusion law admits at least one endemic equilibrium and the model following Chapman's diffusion law has a unique endemic equilibrium. The theoretical results are illustrated by numerical simulations, which additionally show the segregation phenomenon between susceptible and infected populations regulated by different movement strategies. Spatial segregation here is natural, not caused by an isolation policy, and thus is the most important indicator for an infectious disease to spread or wane in the absence of intervention. Several scenarios will be provided to compare different models for spatial segregation and its resulting infection size.