© 2017 Elsevier Inc. Leishmaniasis is a parasite disease transmitted by the bites of sandflies. Cutaneous leishmaniasis is the most common form of the disease and it is endemic in the Americas. Around 70 animal species, including humans, have been found as natural reservoir hosts of leishmania parasites. Among the reservoirs, dogs are the most important ones due to their proximity to the human habitat. Infection by leishmaniasis does not invariably cause illness in the host, and it also can remain asymptomatic for a long period, specially in dogs. In this work we formulate a model to study the transmission of the disease among the vector, humans and dogs. Our main objective is to asses the impact of dogs as a reservoir as well as the impact of asymptomatic humans and dogs on the spread of leishmaniasis. For this end we calculate the Basic Reproduction Number of the disease and we carry out sensitivity analysis of this parameter with respect to the epidemiological and demographic parameters.