Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis : Analysis of a spatially nonlocal model
| Autor: | Junping Shi, Wendi Wang, Stephen A. Gourley, Xiulan Lai, Xingfu Zou, Yanyu Xiao |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0301 basic medicine
education.field_of_study biology Applied Mathematics 030231 tropical medicine Population General Medicine Spread rate Wave speed Tick biology.organism_classification Upper and lower bounds 03 medical and health sciences Computational Mathematics 030104 developmental biology 0302 clinical medicine Spatial model Ixodes scapularis Modeling and Simulation Quantitative Biology::Populations and Evolution Biological dispersal Statistical physics General Agricultural and Biological Sciences education Mathematics |
| Zdroj: | Mathematical Biosciences & Engineering. 15:1033-1054 |
| ISSN: | 1547-1063 |
| DOI: | 10.3934/mbe.2018046 |
| Popis: | yme 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 at least a lower bound for the wave speed in the sense that, if c |
| Databáze: | OpenAIRE |
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