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

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

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.