University of Michigan
Statistical analysis of partially-observed, nonlinear, stochastic spatiotemporal systems is a methodological challenge. Many existing inference algorithms suffer from a "curse of dimensionality" that prohibits their applicability to models describing interacting dynamic processes occurring within and between many spatial locations. New algorithms will be developed, and shown in theory and in practice to advance capabilities for spatiotemporal data analysis. This methodological research will be carried out in the context of addressing a public health concern, transmission of dengue virus. Global incidence of dengue has risen 30-fold over the past fifty years, with notable geographical expansion in South and Central America. The municipality of Rio de Janeiro is a focal point for dengue transmission in this region. Spatiotemporal data on dengue cases in Rio de Janeiro will be analyzed, together with data on human movement, temperature, and rainfall. Policy decisions for the detection, control, and potential eradication of infectious diseases are informed by model-based understanding of disease transmission. Improved understanding of the spatiotemporal dynamics of disease transmission will have implications for improvements in disease control. Mathematical models will be developed to describe spatiotemporal dynamics of dengue transmission, and the novel statistical methodology will be used to link these models to the data from Rio de Janeiro.Spatiotemporal partially-observed Markov process models provide a framework for formulating and answering questions relating spatiotemporal data to an underlying stochastic dynamic process. Statistically efficient inference involves integrating out over possible values of the latent process, a task known as filtering. Except when the system is approximately linear and Gaussian, filtering spatiotemporal models is challenging. One algorithm developed in this project will address the curse of dimensionality by guiding Monte Carlo particles toward important regions in the latent variable space. Another algorithm will combine many weak, independent filters to give a global filtering solution. Disease transmission systems, which are highly nonlinear and stochastic and are imperfectly observable, will be used to motivate and demonstrate the capabilities of the new algorithms. Specifically, models will be developed for the dynamics of dengue transmission in the major metropolis of Rio de Janeiro. Spatiotemporal stochastic epidemiological models will be used to examine the role of human mobility, host immunity, and climate variability in the context of a heterogeneous socioeconomic landscape. A particular goal is to identify locations that function as sources of infection critical to disease invasion and persistence as well as those that act as sinks incapable of sustained local transmission.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.