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.
星期五, 2018/10/05 - 从 10:00 到 12:00