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Cutaneous leishmaniasis in Peru using a vector‐host model: Backward bifurcation and sensitivity analysis
Author(s) -
Barradas Ignacio,
Caja Rivera Rocio Marilyn
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4718
Subject(s) - sandfly , vector (molecular biology) , leishmaniasis , visceral leishmaniasis , bifurcation , mathematics , dengue fever , basic reproduction number , medicine , biology , leishmania , computer science , immunology , environmental health , population , nonlinear system , parasite hosting , biochemistry , physics , quantum mechanics , world wide web , gene , recombinant dna
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 R 0 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 R 0 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.