The control of triatomine populations, vectors of Chagas disease, by spraying insecticides did not prevent the reemergence of the disease. Mathematical models attempt to explain this reemergence by identifying the involved factors in sylvatic transmission of the parasite T.cruzy. In particular, it was revealed that, in addition to vectors, the presence of hosts is essential.

The biological system vector-host is modeled by applying the integrodifference equations. These equations capture, simultaneously, the three processes that are taking place between two successive generations including: demography, infection and spatial dispersal.

The travelling waves, solutions of the integrodifference equations deducted, allow to calculate numerically the invasion speed of the disease. The application of Neubert-Caswell's theorem to calculate the analytical invasion speed seems feasible.

Chagas disease; vector; host; integrodifference equations; travelling waves; invasion speed