Spatial-Temporal Modeling and Estimation of Epidemic Diseases and Invasive Plants Using Hawkes Point Processes

这项研究将为流行病和入侵物种的传播提供新的见解。 特别是，该项目将引入新的、更精确的方法来估计流行病的时空传播。 与基于当前使用的流行病学方法的结果相比，结果也将更加稳健，并且更少依赖于潜在错误的建模假设。 因此，该项目将改进、更准确的估计和预测，并更好地了解与流行病和入侵物种传播相关的政策决策的影响。 这些影响对于防备以及城市规划、保险和公共卫生政策都很重要。 结果将以科学、严谨和负责任的方式传播，尽可能准确地反映传染性或入侵物种带来的真正威胁。 考虑到埃博拉等近期疾病流行对公共卫生的威胁，该项目显得尤为及时。该研究项目利用时空霍克斯点过程模型来表征人类疾病流行和入侵物种传播的动态。 霍克斯模型目前广泛用于地震学中来描述地震目录。 尽管这些模型在地震预报实验中优于竞争对手，并且基于地震像流行病一样传播的概念，通常被称为流行病型余震序列（ETAS）模型，但它们在疾病或入侵物种传播方面的应用却很少。 相反，流行病学家主要使用区室 SIR 模型及其变体，这些模型在用于描述流行病的详细局部行为时可能具有严重的局限性，并且可能会严重高估 SARS 等感染的数量。 事实上，现有的流行病传播率估计基本上依赖于模型，对模型或其参数添加看似微小的变化可能会导致当地危害估计的巨大差异。 该项目将使用和扩展最先进的残差分析技术，例如偏差残差、超细化残差和 Voronoi 残差，以评估现有和拟议模型的拟合优度，并提出改进和改进模型的方法。 最近，修改后的霍克斯模型适用于对哥斯达黎加雨林中蔓延的一种入侵物种红香蕉树的目击，结果证明对于估计移民和时空扩散率、预测以及入侵物种特性的详细描述很有用。 这种类型的点过程分析将扩展到人类疾病流行以及其他入侵物种的研究。 该项目将使用最近开发的统计方法来估计霍克斯点过程模型及其参数，包括用于估计触发函数的非参数技术，而不依赖于触发率的潜在缺陷参数模型，以及显着增加参数估计的稳定性和计算效率的现代积分逼近技术。

This research will provide new insights into the spread of epidemics and invasive species. In particular, this project will introduce new, more precise methods of estimating the spatial-temporal spread of epidemics. The results will also be more robust and less dependent on potentially faulty modeling assumptions compared with those based on currently used epidemiological methods. As a result, the project will lead to improved, more accurate estimations and forecasts, and a better understanding of the impact of policy decisions related to the spread of epidemics and invasive species. Such implications are important for preparedness as well as for urban planning, insurance, and public health policy. The results will be disseminated scientifically, rigorously, and responsibly, reflecting as accurately as possible the true threat presented by infectious or invasive species. This project is especially timely given the public health threat of recent disease epidemics such as Ebola.This research project makes use of spatial-temporal Hawkes point process models to characterize the dynamics of both human disease epidemics and invasive species spread. Hawkes models are currently widely used in seismology to describe earthquake catalogs. Though these models have outperformed their competitors in earthquake forecasting experiments, and are often called Epidemic-Type Aftershock Sequence (ETAS) models based on the notion that earthquakes spread like epidemics, their use in application to the spread of diseases or invasive species has been sparse. Instead, epidemiologists have primarily used compartmental SIR models and their variants, which can have serious limitations when used to describe the detailed local behavior of an epidemic and can significantly overpredict counts of infections such as SARS. Indeed, existing estimates of epidemic spread rates are fundamentally model-dependent, and the addition of seemingly small changes to the models, or their parameters, can result in dramatic differences in local hazard estimates. This project will use and extend state of the art residual analysis techniques, such as deviance residuals, super-thinned residuals, and Voronoi residuals, in order to assess the goodness-of-fit of existing and proposed models and suggest ways to refine and improve them. Recently, a modified Hawkes model was fit to sightings of one invasive species of red banana trees spreading in a Costa Rican rainforest, and the results proved useful for estimating immigration and spatial-temporal spread rates, forecasting, and the detailed description of properties of the invasive species. This type of point process analysis will be extended to the study of human disease epidemics as well as other invasive species. This project will use recently developed statistical methods for estimating Hawkes point process models and their parameters, including non-parametric techniques for estimating the triggering function without relying on potentially flawed parametric models for the triggering rate, as well as modern integral approximation techniques that substantially add stability and computational efficiency to parameter estimates.