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. We are designing new algorithms that we show both in theory and in practice to advance capabilities for spatiotemporal data analysis. This methodological research is being developed in the context of addressing a public health concern, the 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 are being 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 understandings of disease transmission. Improved understanding of the spatiotemporal dynamics of disease transmission will have implications for improvements in disease control. Mathematical models are being developed to describe spatiotemporal dynamics of dengue transmission, and the novel statistical methodology is being 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 we are developing addresses the curse of dimensionality by guiding Monte Carlo particles toward important regions in the latent variable space. Another algorithm combines many weak, independent filters to give a global filtering solution.

Disease transmission systems, which are highly nonlinear, stochastic and imperfectly observable, are used to motivate and demonstrate the capabilities of the new algorithms. Specifically, we are developing models for the dynamics of dengue transmission in the major metropolis of Rio de Janeiro. Spatiotemporal stochastic epidemiological models enable us to examine the roles 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.

The statistical methodology involved builds upon the earlier development of iterated filtering algorithms for inference on a sequence of observations modeled as noisy and incomplete measurements of a latent Markov process with a joint distribution depending on an unknown parameter vector θ. 

This research is supported by a joint NSF/NIH initiative to support research at the interface of the biological and mathematical sciences (grant NSF-DMS-1761603).

By Chensiyuan [CC BY-SA 4.0 (], from Wikimedia Commons