[Mathematical modelling of the propagation of infectious diseases: where we came from, and where we are going].

This work deals with the study of the use of mathematical models to simulate the spreading of infectious diseases. There is no doubt about the importance of the use of computational tools that allow the health staff to model and predict the spreading of an infectious disease. Using such tools one can establish and simulate disease control strategies. The development of such technologies is a multidisciplinary issue; in this sense, the mathematical algorithms -that must be computationally implemented- play a central role. The main goal of this work is to highlight among health community the increasing importance of the use of mathematical models for epidemic disease spreading. Consequently, the main features of such models are introduced and their classification is stated taking into account the behavior, the basic population unit or the mathematical objects used. An exhaustive search of related papers through the most important databases (Medline and Web of Science) are performed. The main conclusion obtained from this work is the central role that mathematical models can play in the simulation of epidemic spreading; moreover,some ideas about the future research are stated.