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

Abstract

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.

Analysis of a Model of Leishmaniasis with Multiple Time Lags in All Populations

“…Various forms of compartmental models for infectious diseases have been formulated [7]. Several models studying the transmission dynamics of CL have been proposed [8][9][10][11][12][13][14]. See [15,16] for a review of mathematical models for visceral leishmaniasis.…”

How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

“…Cutaneous leishmaniasis is a skin infection caused byLeishmania microparasite that is transmitted by female-sandfly bites. 4,5 This neglected disease is the most common form of leishmaniasis, which results in scarring, psychological disorders, and physical disabilities. 6 Yanik et al 7 found that cutaneous leishmaniasis patients with active lesions have the lowest quality of life than that of the other groups because permanent scar formation, social stigmatization produce anxiety, depressive symptoms, decreased body satisfaction, and low quality of life in patients.…”

“…This endemic neglected disease is a worldwide health problem in the Eastern and Western Hemisphere. 4,5,7,8 In the Eastern Hemisphere, cutaneous leishmaniasis is endemic in Asia (Iran, Iraq, Pakistan, India, Afghanistan, Turkmenistan, and Uzbekistan), Africa (Algeria, Sudan, Ethiopia, Kenya, and Egypt), and in Southern Europe (Italy, Portugal, Spain, Ukraine, Bulgaria, Greece, Croatia, and France). In the Western Hemisphere, cutaneous leishmaniasis is endemic in some parts of United States, Mexico, Costa Rica, Nicaragua, Honduras, Brazil, Colombia, Ecuador, Peru, and Venezuela.…”

“…There are relevant mathematical modeling of cutaneous leishmaniasis in previous literature, 4,[14][15][16][17][18][19] but no other has incorporated both characteristics of vector feeding preference and seasonal transmission terms.…”

“…Cutaneous leishmaniasis is a skin infection caused by Leishmania microparasite that is transmitted by female‐sandfly bites . This neglected disease is the most common form of leishmaniasis, which results in scarring, psychological disorders, and physical disabilities .…”