邹幸福教授生物数学系列讲座(二)

发布时间:2018年10月19日 作者:戴斌祥   消息来源:    阅读次数:[]

报告人:中南大学百人计划学者、加拿大西安大略大学邹幸福教授

报告时间:20181023日下午3:00-5:30

报告地点:中南大学数学楼1143教室

报告题目:Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis —— a spatially non-local model

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 talk, I will present 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 maylater drop to the ground, fully fed, at another location. After justifying the well-posedness of the model and analyzing the stability of its steady states, we will 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 turns out to be the minimum wave speed and the actual spread speed of the tick population. We then present some numerical simulation results to demonstrate the above results. We also 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.



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