Mathematical modelling of American cutaneous leishmaniasis: incidental hosts and threshold conditions for infection persistence.

We present a model for the dynamics of transmission of American Cutaneous Leishmaniasis (ACL) that includes a population of incidental hosts for parasites (that is, they act only as sinks of infection), along with species that are reservoir hosts (that is, both source and sink of infection). Although, there is evidence that suggests the existence of incidental hosts for Leishmania parasites, there are no mathematical models developed to account for this. Based on this model we obtained expressions that allow computing the threshold conditions for the persistence of the infection using three different approaches. The three expressions agree in the parameters involved in the computation of the threshold, and also in the parameters that are excluded from it, which are those related to the transmission in incidental hosts. We also suggest alternatives for future development in the modelling of the dynamics of transmission of ACL, according to the needs of a more realistic, precise, or general character of the model.