Space-time modeling and application to emerging infectious diseases

A refined modeling framework for space-time analyses, specifically developed for general Space-Time Autoregressive Moving Average (STARMA) models, is proposed. To enhance accuracy and performance of these analyses, statistical tools and algorithms were extended from univariate case to space-time case, including space-time extensions of the Hannan-Rissanen algorithm, the bias-corrected Akaike information criterion, and the Bayesian information criterion. Methods for assessing statistical significance of model parameters are also presented. A general-purpose statistical software, called Integrated Environment for Analyzing STARMA models (IEAST), is developed for space-time analyses in this research. As an empirical example, the framework and these space-time modeling methods are then applied to investigate the spreading dynamics of West Nile virus (WNV) epidemic in crows and humans in the Detroit Metro area in 2002. Both datasets of dead crows and human cases fit very closely to those expected from a purely STAR (Space-Time Autoregressive) process having low spatial and temporal orders. The use of the STARMA model allows estimation of the rate of spread of WNV at different spatial scales and thus characterization of the expected spatial and temporal scales. In addition, a space-time cross correlation analysis between crow and human cases is conducted. The result shows that there exists high cross correlation between dead crow and human cases at specific spatial and temporal lags. This evidence provides a foundation for the control of human WNV epidemics by using dead crows as a sensitive indicator variable. Statistical inferences from a biological point of view based on these analyses can be used to formulate the prevention and control policies for WNV. The determination of spatial-temporal autoregressive parameters using STARMA holds considerable promise for characterizing emerging infectious diseases.