報告題目：Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis: analysis of a spatially nonlocal model
報告人：鄒幸福 教授
報告時間：2021年3月20日（星期六）上午9:30-10:30
騰訊會議：965 227 339
報告摘要：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.
鄒幸福教授簡介: 鄒幸福教授分別在中山大學，湖南大學和約克大學(York University，Canada)獲得學士，碩士和博士學位，並在維多利亞大學（University of Victoria, Canada）和佐治亞理工(Georgia Institute of Technology, USA)從事過博士後研究工作。曾任教於加拿大紐芬蘭紀念大學（Memorial University of Newfoundland, Canada）， 現為加拿大西安大略大學（University of Western Ontario）應用數學系的教授。2012年入選湖南省“百人計劃”專家並在中南大學擔任特聘教授。研究興趣為微分方程和動力系統的理論及應用，特別是反應擴散方程、常泛函微分方程及偏泛函微分方程及其在生物領域的應用.在J. Diff. Eqns.、SIAM J. Appl. Math.、SIAM J. Math. Anal.等著名雜誌發表有影響的研究論文100余篇，擔任Applicable Analysis、Journal of Computational and AppliedMathematics、Communications on Pure and Applied Analysis等SCI收錄雜誌的編委，曾獲加拿大國家自然科學和工程基金博士後獎，Petro-Canada青年研究創新獎，安大略省長傑出研究獎。