Cutaneous leishmaniasis in Peru using a vector‐host model: Backward bifurcation and sensitivity analysis

The final goal of control policies in neglected vector-borne diseases in developing countries is to protect humans. These vector-borne diseases include leishmaniasis, dengue, chagas, and malaria. The traditional control measures for vector-borne diseases, as with any other illnesses, suggest to reduce the basic reproduction number R0 below the value 1. This strategy is not necessarily sufficient when a backward bifurcation occurs. Because of its worldwide relevance, we are interested in modeling cutaneous leishmaniasis with Peru as a specific example. We use a vector-host model with an extrinsic incubation period, which gives evidence that a backward bifurcation can occur under certain conditions. We estimate some parameters for the cutaneous leishmaniasis model in Peru. The uncertainty of the parameters suggests that we cannot guarantee the avoidance of a backward bifurcation range. It is important to be attentive to the appearance of phenomena that could make eradication more difficult. Local and global sensitivity analyses agree that R0 is most sensitive to the number of bites by a female sandfly and its natural mortality rate. The former dependency suggests very practical control policies.