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In this paper we describe a recently developed algorithm called Topological Weighted Centroid (TWC). TWC takes locations of an event of interest and analyzes the possible associated dynamics using the ideas of free energy and entropy. This novel mathematical tool has been applied to a real world example, the epidemic outbreak caused by Escherichia coli that occurred in Germany in 2011, to point out the real source of the outbreak. Other four examples of application to other epidemic spreads are described: Chikungunya fever of 2007 in Italy; Foot and mouth disease of 1967 in England; Cholera of 1854 in London; and the Russian influenza of 1889–1890 in Sweden. Comparisons have been made with other already published algorithms: Rossmo Algorithm, NES, LVM, Mexican Prob. The TWC results are significantly superior in comparison with other algorithms according to four independent indexes: distance from the peak, sensitivity, specificity and searching area. They are consistent with the idea that the spread of infectious disease is not random but follows a progression based on inherent, but as yet undiscovered, mathematical laws. The TWC method could provide an additional powerful tool for the investigation of the early stages of an epidemic and novel simulation methods for understanding the process through which a disease is spread.