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Models on the population dynamics of Chagas disease are discussed. The effects of vector and blood transfusion transmission are considered and epidemiological data is provided to support model assumptions. Also, the role of density-dependence on the population dynamics of the vector population is explored as well as the existence of non-reproductive insect stages involved in the transmission process. When density dependent effects are neglected, there is a non-oscillatory approach to the endemic equilibrium (local asymptotic stability). When density-dependence effects and vector stage-structure are introduced, limit cycle solutions may be obtained. Results are compared to available field data.