标题： 空间波的建模用于控制蚊媒疾病的沃尔巴克氏体入侵 显示英文标题

标题： Modeling spatial waves of Wolbachia invasion for controlling mosquito-borne diseases

摘要： 沃尔巴克氏体是一种天然细菌，可以感染蚊子并降低其传播蚊媒疾病的能力，如登革热、寨卡病毒和基孔肯雅热。 现场试验和建模研究显示，蚊子中的感染比例必须超过一个临界水平，感染才能持续存在。 为了捕捉这个临界值，必须考虑由感染蚊子局部释放所造成的感染蚊子和未感染蚊子分布的空间异质性。 我们开发并分析了偏微分方程（PDE）模型，以研究沃尔巴克氏体感染在野外蚊子中的入侵动态。 我们的反应扩散型模型考虑了复杂的垂直传播和空间蚊子扩散。 我们描述了成功入侵的临界条件，这是一个称为“临界泡”的泡状轮廓。 与一维景观中其他空间轮廓相比，临界泡在其释放尺寸上是最优的。 在释放中心附近的感染比例高于相应均匀混合常微分方程（ODE）模型的临界水平。 我们表明，当超过临界值时，所提出的空间模型会产生沃尔巴克氏体感染的行波。 我们量化了临界条件和行波速度如何依赖于扩散系数和其他模型参数。 给出了不同情景的数值研究，以指导释放策略的设计。 显示英文摘要

摘要： Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes, which is created by the local release of the infected mosquitoes. We develop and analyze partial differential equation (PDE) models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for both the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion, which is a bubble-shaped profile, called the "critical bubble". The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies.