报告题目：Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis: analysis of a spatially nonlocal model
腾讯会议：965 227 339
报告摘要：Lyme disease is transmitted via blacklegged ticks, the spatial spread of which is believed to be primarily via transport on white-tailed deer. In this paper, we develop a mathematical model to describe the spatial spread of blacklegged ticks due to deer dispersal. The model turns out to be a system of differential equations with a spatially non-local term accounting for the phenomenon that a questing female adult tick that attaches to a deer at one location may later drop to the ground, fully fed, at another location having been transported by the deer. We first justify the well-posedness of the model and analyze the stability of its steady states. We then explore the existence of traveling wave fronts connecting the extinction equilibrium with the positive equilibrium for the system. We derive an algebraic equation that determines a critical value which is then proved to be (i) the minimal speed of traveling wave fronts in the sense that for , there is a traveling wave front of speed c connecting the extinction steady state to the positive steady state; and for , there is no such traveling wave front; and (ii) the actually spread speed when initial distribution has compact support. We also carry out some numerical simulations for the original spatial model system and the results seem to confirm that the actual spread rate of the tick population coincides with . We also numerically explore the dependence of on the dispersion rate of the white tailed deer, by which one may evaluate the role of the deer's dispersion in the geographical spread of the ticks.
邹幸福教授简介: 邹幸福教授分别在中山大学，湖南大学和约克大学(York University，Canada)获得学士，硕士和博士学位，并在维多利亚大学（University of Victoria, Canada）和佐治亚理工(Georgia Institute of Technology, USA)从事过博士后研究工作。曾任教于加拿大纽芬兰纪念大学（Memorial University of Newfoundland, Canada）， 现为加拿大西安大略大学（University of Western Ontario）应用数学系的教授。2012年入选湖南省“百人计划”专家并在中南大学担任特聘教授。研究兴趣为微分方程和动力系统的理论及应用，特别是反应扩散方程、常泛函微分方程及偏泛函微分方程及其在生物领域的应用.在J. Diff. Eqns.、SIAM J. Appl. Math.、SIAM J. Math. Anal.等著名杂志发表有影响的研究论文100余篇，担任Applicable Analysis、Journal of Computational and AppliedMathematics、Communications on Pure and Applied Analysis等SCI收录杂志的编委，曾获加拿大国家自然科学和工程基金博士后奖，Petro-Canada青年研究创新奖，安大略省长杰出研究奖。