題 目：Role of of white-tailed deer in geographic spread of blacklegged tick: a spatially nonlocal model and its analysis
内容簡介：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 c* which is then proved to be (i) the minimal speed of traveling wave fronts in the sense that for c > c*, there is a traveling wave front of speed c connecting the extinction steady state to the positive steady state; and for c<c*, 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 confirm the role of c^* described above. We also numerically explore the dependence of c^* 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.
報告人：鄒幸福
報告人簡介：鄒幸福教授分别在中山大學、湖南大學和加拿大York University獲得學士、碩士和博士學位，并在加拿大University of Victoria和美國Georgia Institute of Technology 從事過博士後研究工作。曾任教于加拿大Memorial University of Newfoundland，現為加拿大University of Western Ontario數學系教授。研究興趣為微分方程和動力系統的理論及應用，特别是反應擴散方程、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。
時 間：2022年12月22日（周四）上午 9：00 始
地 點：騰訊會議ID：954-544-985
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