Chagas disease is caused by the protozoan Trypanosoma cruzi, which parasitizes many mammals, including humans. Its vectors are blood-feeding hematophagous triatomine insects of different species, which vary according to the geographical area. One of the 17 neglected diseases targeted by the World Health Organization, Chagas disease is endemic to the Americas, but has spread to other countries due to human migratory movements. In this study, we describe the epidemiological dynamics of Chagas disease in an endemic area, considering the main transmission mechanisms and the demographic effects of birth, mortality, and human migration in this phenomenon. We apply mathematical models as a methodological approach to simulate the interactions between reservoirs, vectors, and humans using a system of ordinary differential equations. The results show that the Chagas disease control measures currently in place cannot be relaxed without endangering the progress achieved to date.