Chagas disease is endemic to tropical-rural areas and has become a public health problem in Latin America (from Patagonia to the southern United States). The World Health Organization estimates that 17 million people are infected and 100 million more are at risk of infection. Considering the routes of transmission, it has spread to non-endemic regions of Europe and the United States. The chronic phase of the disease has an average duration of 15 years and there are no appropriate drugs or vaccines available to treat it; during this period those infected develop stroke and neurological disorders, as well as severe inflammation in their intestines, esophagus and heart, the latter being the cause of highest mortality. Bearing in mind the scarce knowledge of the dynamics of the disease dispersion, a study of the dispersion in humans was carried out in a non-endemic area of Colombia. The computational technique "Cellular Automata" was implemented to predict the number of infected people and their geographical distribution in the study region, taking into account the sexual, congenital and transfusion transmission routes.