Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modeling and analyzing the transmission dynamics of visceral leishmaniasis

1. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2. Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA

In this paper, we develop a mathematical model to study the transmission dynamics of visceral leishmaniasis. Three populations: dogs, sandflies and humans, are considered in the model. Based on recent studies, we include vertical transmission of dogs in the spread of the disease. We also investigate the impact of asymptomatic humans and dogs as secondary reservoirs of the parasites. The basic reproduction number and sensitivity analysis show that the control of dog-sandfly transmission is more important for the elimination of the disease. Vaccination of susceptible dogs, treatment of infective dogs, as well as control of vertical transmission in dogs are effective prevention and control measures for visceral leishmaniasis.

  Article Metrics

Keywords Visceral leishmaniasis; mathematical modeling; reservoir; vertical transmission; basic reproduction number

Citation: Lan Zou, Jing Chen, Shigui Ruan. Modeling and analyzing the transmission dynamics of visceral leishmaniasis. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1585-1604. doi: 10.3934/mbe.2017082


  • [1] D. A. Ashford,J. R. David,M. Freire,R. David,I. Sherlock,M. D. C. Eulalio,D. P. Sampaio,R. Badaro, Studies on control of visceral leishmaniasis: Impact of dog control on canine and human visceral leishmaniasis in Jacobina, Bahia, Brazil, Am. J. Trop. Med. Hyg., 59 (1998): 53-57.
  • [2] P. M. Boggiatto, K. N. Gibson-Corley and K. Metz, et. al., Transplacental transmission of Leishmania infantum as a means for continued disease incidence in North America, PLoS Negl. Trop. Dis. , 5 (2011), e1019.
  • [3] P. M. Boggiatto,A. E. Ramer-Tait,K. Metz, Immunologic indicators of clinical progression during canine Leishmania infantum infection, Clin. Vaccine Immunol., 17 (2010): 267-273.
  • [4] M. N. Burrattini,F. B. A. Cuoutinho,L. F. Lopez,E. Massad, Modeling the dynamics of leishmaniasis considering human, animal host and vector populations, J. Biol. Sys., 6 (1998): 337-356.
  • [5] Chinese Center for Disease Control and Prevention, Public Health Data Center, 2004-2013, Available from: http://www.phsciencedata.cn/Share/index.jsp.
  • [6] O. Courtenay, C. Carson, L. Calvo-Bado, L. M. Garcez and R. J. Quinnell, Heterogeneities in Leishmania infantum infection: using skin parasite burdens to identify highly infectious dogs, PLoS Negl. Trop. Dis., 8 (2014), e2583.
  • [7] C. Dye, The logic of visceral leishmaniasis control, Am. J. Trop. Med. Hyg., 55 (1996): 125-130.
  • [8] I. M. ELmojtaba,J. Y. T. Mugisha,M. H. A. Hashim, Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan, Appl. Math. Comput., 217 (2010): 2567-2578.
  • [9] K. J. Esch,N. N. Pontes,P. Arruda,A. O'Connor,L. Morais,S. M. Jeronimo,C. A. Petersen, Preventing zoonotic canine leishmaniasis in northeastern Brazil: Pet attachment and adoption of community leishmania prevention, Am. J. Trop. Med. Hyg., 87 (2012): 822-831.
  • [10] L. Gradoni, Canine leishmania vaccines: Still a long way to go, Vet. Parasitol., 208 (2015): 94-100.
  • [11] T. Grinnage-Pulley, B. Scott and C. A. Petersen, A mother's gift: Congenital transmission of Trypanosoma and Leishmania species, PLoS Pathog., 12 (2016), e1005302.
  • [12] N. Hartemink, S. O. Vanwambeke, H. Heesterbeek, D. Rogers, D. Morley, B. Pesson, C. Davies, S. Mahamdallie and P. Ready, Integrated mapping of establishment risk for emerging vector-borne infections: A case study of canine leishmaniasis in southwest France, PLoS One, 6 (2011), e20817.
  • [13] G. Hasibeder,C. Dye,J. Carpenter, Mathematical modeling and theory for estimating the basic reproduction number of canine leishmaniasis, Parasitol., 105 (1992): 43-53.
  • [14] Imperial College London, Theoretical Immunology Group Resources, Sand fly fact sheet, Available from: http://wwwf.imperial.ac.uk/theoreticalimmunology/exhibit2010/pdf/fs-sandflies.pdf.
  • [15] S. F. Kerr,W. E. Grant,N. O. Dronen Jr, A simulation model of the infection cycle of Leishmania mexicana in Neotoma microbus, Ecol. Model., 98 (1997): 187-197.
  • [16] Länger, et. al., Modeling of leishmaniasis infection dynamics: Novel application to the design of effective therapies, BMC Syst. Biol., 6 (2012), 1.
  • [17] I. D. Lima,J. W. Queiroz,H. G. Lacerda, Leishmania infantum chagasi in northeastern Brazil: Asymptomatic infection at the urban perimeter, Am. J. Trop. Med. Hyg., 86 (2012): 99-107.
  • [18] L. V. R. Lima,L. A. Carneiro,M. B. Campos, Canine visceral leishmaniasis due to Leishmania (L.) infantum chagasi in Amazonian Brazil: comparison of the parasite density from the skin, lymph node and visceral tissues between symptomatic and asymptomatic, seropositive dogs, Revista Institut. Med. Trop. Sao Paulo, 52 (2010): 259-265.
  • [19] G. Michel,C. Pomares,B. Ferrua,P. Marty, Importance of worldwide asymptomatic carriers of leishmania infantum (L. chagasi) in human, Acta Trop., 119 (2011): 69-75.
  • [20] R. Molina,J. M. Lohse,F. Pulido, Infection of sandflies by humans co-infected with leishmania infantum and human immuneodeficiency virus, Amer. J. Trop. Med. Hyg., 60 (1999): 51-53.
  • [21] T. J. Naucke,S. Lorentz, Non-sandfly transmission of canine leishmaniasis, Tieraerztliche Umschau, 68 (2013): 121-125.
  • [22] C. B. Palatnik-de-Sousa,I. Silva-Antunes,A. Morgado,I. Menz,M. Palatnik,C. Lavor, Decrease of the incidence of human and canine visceral leishmaniasis after dog vaccination with leishmune in Brazilian endemic areas, Vaccine, 27 (2009): 3505-3512.
  • [23] R. Reithinger,P. G. Coleman,B. Alexander, Are insecticide-impregnated dog collars a feasible alternative to dog culling as a atrategy for controlling canine visceral leishmaniasis in Brazil?, Int. J. Parasitol., 34 (2004): 55-62.
  • [24] G. A. Romero and M. Boelaert, Control of visceral leishmaniasis in Latin America -a systematic revies, PLoS Negl. Trop. Dis., 4 (2010), e584.
  • [25] A. Stauch, R. R. Sakar and A. Picado, et. al., Visceral leishmaniasis in the Indian subcontinent: Modelling epidemiology and control, PLoS Negl. Trop. Dis., 5 (2011), e1405.
  • [26] P. van den Driessche,J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002): 29-48.
  • [27] J. Wang, Y. Ha and C. Gao, et al., The prevalence of canine Leishmania infantum infection in western China detected by PCR and serological tests, Parasit. Vectors, 4 (2011), 69.
  • [28] J. Wang,C. Gao,Y. Yang, An outbreak of the desert sub-type of zoonotic visceral leishmaniasis in Jiashi, Xinjiang Uygur Autonomous Region, People's Republic of China, Parasitol. Int., 59 (2010): 331-337.
  • [29] The World Bank Group, Population, total, 2015, Available from: http://data.worldbank.org/indicator/SP.POP.TOTL?locations=BR.
  • [30] World Health Organization, Number of cases of visceral leishmaniasis reported data by country, Available from: http://apps.who.int/gho/data/node.main.NTDLEISHVNUM?lang=en.
  • [31] World Health Organization, Available from: http://www.who.int/leishmaniasis/resources/BRAZIL.pdf.
  • [32] World Health Organization, World Health Organization, Leishmaniasis in high-burden countries: An epidemiological update based on data reported in 2014, Weekly Epid. Record, 91 (2016): 287-296.
  • [33] S. Zhao,Y. Kuang,C. Wu,D. Ben-Arieh,M. Ramalho-Ortigao,K. Bi, Zoonotic visceral leishmaniasis transmission: Modeling, backward bifurcation, and optimal control, J. Math. Biol., 73 (2016): 1525-1560.


This article has been cited by

  • 1. Kaiming Bi, Yuyang Chen, Songnian Zhao, Yan Kuang, Chih-Hang John Wu, Current Visceral Leishmaniasis Research: A Research Review to Inspire Future Study, BioMed Research International, 2018, 2018, 1, 10.1155/2018/9872095
  • 2. Ana Izabel Passarella Teixeira, Debora Marcolino Silva, Tamires Vital, Nadjar Nitz, Bruna Caroline de Carvalho, Mariana Hecht, Diana Oliveira, Edward Oliveira, Ana Rabello, Gustavo Adolfo Sierra Romero, Improving the reference standard for the diagnosis of canine visceral leishmaniasis: a challenge for current and future tests, Memórias do Instituto Oswaldo Cruz, 2019, 114, 0, 10.1590/0074-02760180452
  • 3. Angela J. Toepp, Carolyne Bennett, Benjamin Scott, Reid Senesac, Jacob J. Oleson, Christine A. Petersen, Mary Ann McDowell, Maternal Leishmania infantum infection status has significant impact on leishmaniasis in offspring, PLOS Neglected Tropical Diseases, 2019, 13, 2, e0007058, 10.1371/journal.pntd.0007058
  • 4. Kamil Erguler, Irene Pontiki, George Zittis, Yiannis Proestos, Vasiliki Christodoulou, Nikolaos Tsirigotakis, Maria Antoniou, Ozge Erisoz Kasap, Bulent Alten, Jos Lelieveld, A climate-driven and field data-assimilated population dynamics model of sand flies, Scientific Reports, 2019, 9, 1, 10.1038/s41598-019-38994-w
  • 5. Muhammad Altaf Khan, Olusola Kolebaje, Ahmet Yildirim, Saif Ullah, P. Kumam, P. Thounthong, Fractional investigations of zoonotic visceral leishmaniasis disease with singular and non-singular kernel, The European Physical Journal Plus, 2019, 134, 10, 10.1140/epjp/i2019-12861-1

Reader Comments

your name: *   your email: *  

Copyright Info: 2017, Lan Zou, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved