  This paper offers the first systematic presentation of the topological
approach to the analysis of epidemic and pseudo-epidemic spatial processes. We
introduce the basic concepts and proofs, at test the approach on a diverse
collection of case studies of historically documented epidemic and
pseudo-epidemic processes. The approach is found to consistently provide
reliable estimates of the structural features of epidemic processes, and to
provide useful analytical insights and interpretations of fragmentary
pseudo-epidemic processes. Although this analysis has to be regarded as
preliminary, we find that the approach's basic tenets are strongly corroborated
by this first test and warrant future research in this vein.
