论文标题
PDE-ode耦合的时空数学模型，用于盛开期间的火疫病
A PDE-ODE Coupled Spatio-Temporal Mathematical Model for Fire Blight During Bloom
论文作者
论文摘要
消防疫病是一种影响苹果树和梨树的细菌植物疾病。我们提出了一种数学模型，用于在花期间在果园中蔓延。这是一个PDE-ode耦合系统，由病原体的两个半线性PDE组成，与固定宿主的三个ODES耦合。探索性数值模拟表明，使用上限和下限的方法以及Schauder的固定点定理，在某些条件下，我们随后在某些条件下证明了行进波。我们的结果可能不是最佳的，因为我们对参数的约束（可以在生物学上解释）足以存在于行进波的存在，但可能不是必需的。讨论了对消防疫病生物学和管理的可能影响。
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.
