TRAVELLING WAVES IN INVASION PROCESSES WITH PATHOGENS
TRAVELLING WAVES IN INVASION PROCESSES WITH PATHOGENS
复制标题
病原体入侵过程中的行波
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Langlais
中科院分区：
文献类型：
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作者：
A. Ducrot;M. Langlais
这项工作是致力于研究一个奇异的反应扩散系统中所产生的建模引入一个致命的病原体入侵的主机人口。在没有病原体的情况下，宿主种群表现出一种动态的（或Allee效应）。考虑中的奇异SI模型的早期数值模拟已经表现出稳定的行波，并且在某些情况下，由于病原体的引入，波前速度发生逆转。在这里，我们证明了这种行波解的存在，研究其线性稳定性，并给出分析条件，产生一个逆转的波前速度，即入侵的主机人口可能最终撤退后引入的致命病原体。
This work is devoted to the study of a singular reaction–diffusion system arising in modelling the introduction of a lethal pathogen within an invading host population. In the absence of the pathogen, the host population exhibits a bistable dynamics (or Allee effect). Earlier numerical simulations of the singular SI model under consideration have exhibited stable travelling waves and also, under some circumstances, a reversal of the wave front speed due to the introduction of the pathogen. Here we prove the existence of such travelling wave solutions, study their linear stability and give analytical conditions yielding a reversal of the wave front speed, i.e. the invading host population may eventually retreat following the introduction of the lethal pathogen.