Disease transmission is difficult to model because most vectors and hosts have different generation times. Chagas disease is such a situation, where insect vectors have 1–2 generations annually and mammalian hosts, including humans, can live for decades. The hemataphagous triatominae vectors (Hemiptera: Reduviidae) of the causative parasite Trypanosoma cruzi (Kinetoplastida: Trypanosomatidae) usually feed on sleeping hosts, making vector infestation of houses, peridomestic areas, and wild animal burrows a central factor in transmission. Because of difficulties with different generation times, we developed a model considering the dwelling as the unit of infection, changing the dynamics from an indirect to a direct transmission model. In some regions, vectors only infest houses; in others, they infest corrals; and in some regions, they also infest wild animal burrows. We examined the effect of sylvatic and peridomestic vector populations on household infestation rates. Both sylvatic and peridomestic vectors increase house infestation rates, sylvatic much more than peridomestic, as measured by the reproductive number R₀. The efficacy of manipulating parameters in the model to control vector populations was examined. When R₀ > 1, the number of infested houses increases. The presence of sylvatic vectors increases R₀ by at least an order of magnitude. When there are no sylvatic vectors, spraying rate is the most influential parameter. Spraying rate is relatively unimportant when there are sylvatic vectors; in this case, community size, especially the ratio of houses to sylvatic burrows, is most important. The application of this modeling approach to other parasites and enhancements of the model are discussed.