A traveling epidemic model of space–time disease spread

Abstract

This work presents a random field model of disease attribute (incidence, mortality etc.) that transfers the study of the attribute distribution from the original spatiotemporal domain onto a lower-dimensionality traveling domain that moves along the direction of disease velocity. The partial differential equations connecting the disease attribute covariances in the original and the traveling domain are derived with coefficients that are functions of the disease velocity. These equations offer epidemiologic insight concerning the strength of the space–time dependence between the disease attribute values in the two domains. The traveling disease model has certain theoretical and computational advantages in the study and prediction of space–time disease attribute distributions in conditions of uncertainty. Estimates of the disease attribute are derived in the traveling domain and then used to generate maps of space–time disease attribute distribution in the original domain. The theoretical model is illustrated and additional insight is gained by means of a numerical mortality simulation study, which shows that the proposed model is at least as accurate but computationally more efficient than mainstream mapping techniques of higher dimensionality. These findings concerning the very good predictability of the proposed model also strongly support its adequacy to represent the space–time mortality distribution.