Some of the vector-borne infections with public health importance involve an animal reservoir. This work describes, through a compartimental model, the dynamics of leishmaniasis considering the interactions between the three populations involved, namely the sandfly, the domestic dog (as the principal intermediate host), and the human population. An expression for the Basic Reproduction Ratio (R 0 ), which takes into account the time delay representing the extrinsic incubation period of the parasite in the vector, is presented. Numerical simulation, equilibrium and stability analysis provided insights into the transmission dynamics of the infection that can help in the design of control strategies.
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Burattini et al. (1998) studied this question.