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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.27 n.1 San José Jan./Jun. 2020

http://dx.doi.org/10.15517/rmta.v27i1.39973 

Artículo

Modeling Post-Kala-Azar dermal Leishmaniasis as an infection reservoir for visceral Leishmaniasis

Leishmaniasis dérmica Post-Kala-Azar como reservorio de infección para la Leishmaniasis visceral

Andrea Calderon1 

Ryan Landrith2 

Nhan Le3 

Ileana Muñoz4 

Christopher M. Kribs5 

1University of Texas at Arlington; Department of Biology; Arlington TX; United States; andrea.calderon@mavs.uta.edu

2University of Texas at Arlington, Department of Biology, Arlington TX, United States; ryan.landrith@mavs.uta.edu

3University of Texas at Arlington, Department of Computer Science and Engineering, Arlington TX, United States; nhan.le@mavs.uta.edu

4University of Texas at Arlington, Department of Mathematics, Arlington TX, United States; ileana.munoz@mavs.uta.edu

5University of Texas at Arlington, Departments of Mathematics and Curriculum & Instruction, Arlington TX, United States; kribs@uta.edu

Abstract

Visceral Leishmaniasis (VL) is a potentially fatal disease caused by the protozoan parasite Leishmania donovani. This disease is a health problem for the very poor because it results in thousands of deaths and illnesses every year. Some countries, such as India and Bangladesh, have started programs to reduce the occurrences of VL by focusing on early diagnosis and complete treatment of VL. Post-Kala-azar Dermal Leishmaniasis (PKDL) is a cutaneous manifestation of Leishmaniasis that can occur following the incomplete treatment of VL. Diagnosis and treatment of PKDL are limited in affected regions, and PKDL has been identified as a possible reservoir for infection. This study develops a mathematical model of the relationship between the level of PKDL treatment and the incidences of VL during a given period. The results indicate a nearly linear relationship between PKDL treatment rates and the percent reduction of VL incidences. With the current treatments available and considering achievable levels of treatment, the model predicts that up to 20% of VL cases could be prevented by treating new PKDL cases. Hypothetical combined treatment initiatives including bed nets and insecticide spraying are also considered. Results suggest that the population of individuals with PKDL is certainly a significant factor in the transmission of L. donovani infection, with treatment of new cases particularly important.

Keywords: disease reservoir; experimental treatment; sandfly vector.

Resumen

La leishmaniasis visceral (VL) es una enfermedad potencialmente mortal causada por el parásito protozoario Leishmania donovani. Esta enfermedad es un problema de salud para los muy pobres porque da lugar a miles de muertes e infecciones cada año. Algunos países, como la India y Bangladesh, han comenzado programas para reducir las ocurrencias de VL centrándose en el diagnóstico precoz y el tratamiento completo de la VL. La leishmaniasis dérmica post-kala-azar (PKDL) es una manifestación cutánea de la leishmaniasis que puede ocurrir después del tratamiento incompleto de la VL. El diagnóstico y el tratamiento de PKDL son limitados en las regiones afectadas, y PKDL se ha identificado como un posible reservorio para la infección. Este estudio desarrolla un modelo matemático de la relación entre el nivel de tratamiento de PKDL y las incidencias de VL durante un periodo determinado. Los resultados indican una relación casi lineal entre las tasas de tratamiento de PKDL y la reducción porcentual de incidencias de VL. Con los tratamientos actualmente disponibles y teniendo en cuenta los niveles alcanzables de tratamiento, el modelo predice que hasta 20% de los casos de VL podrían prevenirse mediante el tratamiento de nuevos casos PKDL. También se tienen en cuenta iniciativas de tratamiento combinadas hipotéticas, como mosquiteros y pulverización de insecticidas. Los resultados sugieren que la población de individuos con PKDL es sin duda un factor importante en la transmisión de L. donovani, con el tratamiento de nuevos casos particularmente importantes.

Palabras clave: reservorio de enfermedad; tratamiento experimental; vector flebótomo.

Mathematics Subject Classification: 92C37.

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Acknowledgements

This research was supported by an NSF UBM-Institutional grant, DUE#0827136, as part of the UTTER program at UT Arlington

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Received: May 16, 2019; Revised: June 06, 2019; Accepted: September 13, 2019

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