花期梨火疫病的PDE-ODE耦合时空数学模型
A PDE-ODE Coupled Spatio-Temporal Mathematical Model for Fire Blight During Bloom
AI总结：
本文提出了花期梨火疫病传播的PDE-ODE耦合时空数学模型，通过上下界方法和Schauder不动点定理证明了行波解的存在性，并讨论了其生物学与管理意义。
摘要：
梨火疫病是一种影响苹果树和梨树的细菌性植物疾病。我们提出了一个关于其在果园花期传播的数学模型。这是一个PDE-ODE耦合系统，由描述病原体的两个半线性PDE与描述固定宿主的三个ODE系统耦合而成。探索性数值模拟表明行波的存在性，随后我们在参数满足一定条件的情况下，利用上下界方法和Schauder不动点定理对其进行了证明。我们的结果可能并非最优，因为我们对参数的约束（具有生物学解释）是行波存在的充分条件，但可能并非必要条件。本文还讨论了这些结果对梨火疫病生物学和管理的潜在影响。
英文摘要：
Fire blight is a bacterial plant disease that affects apple and pear trees. We present a mathematical model for its spread in an orchard during bloom. This is a PDE-ODE coupled system, consisting of two semilinear PDEs for the pathogen, coupled to a system of three ODEs for the stationary hosts. Exploratory numerical simulations suggest the existence of travelling waves, which we subsequently prove, under some conditions on parameters, using the method of upper and lower bounds and Schauder's fixed point theorem. Our results are likely not optimal in the sense that our constraints on parameters, which can be interpreted biologically, are sufficient for the existence of travelling waves, but probably not necessary. Possible implications for fire blight biology and management are discussed.
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