Abstract
The aim of this work is to understand the spatial spread of Chagas disease, which is primarily transmitted by triatomines. We propose a mathematical model using a system of partial differential reaction–diffusion equations to study and describe the spread of this disease in the human population. We consider the respective subclasses of infected and uninfected individuals within the human and triatomine populations. The dynamics of the infected human subpopulation considers two disease phases: acute and chronic. The human population is considered to be homogeneously distributed across a space to describe the local propagation of Chagas disease by triatomines during a short epidemic period. We determine the basic reproduction number that allows us to assess Chagas disease control measures, and we determine the speed of disease propagation by using traveling wave solutions for our model.
Similar content being viewed by others
References
Argolo AM, Felix M, Pacheco R, Costa J (2008) Doença de Chagas e seus principais vetores no Brasil. Imperial Novo Milênio, Inst Oswaldo Cruz, Rio de Janeiro
Abrahan LB, Gorla DE, Catalá SS (2011) Dispersal of Triatoma infestans and other triatominae species in the arid Chaco of Argentina—flying, walking or passive carriage? The importance of walking females. Mem Inst Oswaldo Cruz 106(2):232–239
Castañera MB, Aparicio JP, Gürtler RE (2003) A age stage-structured stochastic model of the popualtion dynamic of Triatoma infestans, the main vector of Chagas disease. Ecol Model 162:33–53
Catala S, Crocco LB, Morales GF (1997) Trypanosoma cruzi transmission risk index (TcTRI): an epidemiological indicator of Chagas disease vectorial transmission to human. Acta trop 68:285–295
Crawford BA, Kribs-Zaleta CM (2013a) Vetor migration and dispersal rates for sylvatic T. cruzi transmission. Ecol Complex 14:145–156
Crawford BA, Kribs-Zaleta CM, Ambartsoumian G (2013b) Invasion speed in cellular automaton models for T. cruzi vector migration. Bull Math Biol 75:1052–1081
Crawford BA, Kribs-Zaleta CM (2014) A metapopualtion model for T. cruzi sylvatic transmission with vector migration. Math Biosci Eng 11(3):471–509
Cohen JE, Gürtler RE (2001) Modeling household transmission of American trypanosomiasis. Science 293:694698
Cruz-Pacheco G, Esteva L, Vargas C (2012) Control measures for Chagas disease. Math Biosci 237:49–69
Das P, Mukherjee D (2006) Qualitative study of a model of Chagas disease. Math Comput Model 43:413–422
Dias JCP, Coura JR (1997) Clínica e terapêutica da doença de chagas: uma abordagem prática para o clínico geral. SciELO- Editora FIOCRUZ, Rio de Janeiro
EMedicine (Medscape) (2016) Chagas disease (American trypanosomiasis). http://emedicine.medscape.com/article/214581-overview
Forattini OP, Rabello EX, Pattoli DBG (1972) Aspectos ecológicos da Tripanossomose Americana, IV— mobilidade de Triatoma arthurneivai em seus ecótopos naturais. Rev Saúd Públ 6:183–187
Fundação Oswaldo Cruz (2014) http://www.fiocruz.br/ioc/cgi/cgilua.exe/sys/start.htm?infoid=1585&sid=32
Howard EJ, Xiong X, Carlier Y, Sosa-Estani S, Buekens P (2014) Frequency of the congenital transmission of Trypanosoma cruzi: a systematic review and meta-analysis. BJOG 121(1):22–33. https://doi.org/10.1111/1471-0528.12396
Instituto Brasileiro de Geografia estátisitica (IBGE) (2017) https://www.ibge.gov.br
Institute for One World Health (2014) Chagas disease: a Latin American nemesis. http://s3.amazonaws.com/zanran_storage/www.oneworldhealth.org/ContentPages/15710128.pdf
Kribs-Zaleta C (2010) Estimating contact process saturation in sylvatic transmission of Trypanosoma cruzi in the United States. PLoS Negl Trop Dis 4(4):1–13
Lazzari CR, Pereira MH, Lorenzo MG (2013) Behavioural biology of Chagas disease vectors. Mem Inst Oswaldo Cruz 108(Suppl. 1):34–47
Martcheva M (2015) An introduction to mathematical epidemiology. Springer, Berlin
Mesk M, Mahdjoub T, Gourbière S, Rabinovich JE, Menu F (2016) Invasion speeds of Triatoma dimidata, vector of Chagas disease: an application of orthogonal polynomials method. J Theor Biol 395:126–143
Montoya R, Dias JCP, Coura JR (2003) Chagas disease in a community in southeast Brazil. I. A serologic follow-up study on a vector controlled area. Rev Inst Med Trop Sao Paulo 45(5):269–274
Murray JD (2002) Mathematical biology. Springer, Berlin
Murray JD, Stanley FRS, Brown DL (1986) On the spatial spread of rabies among foxes. Proc R Soc Lond Ser B 229:111–150
Nunes EV, Campos R, Socorro CG, Tolezano JE, Moreira AAB, Souza HBW, Takiguti CK, Neto VA (1991) O xenodiagnóstico na doena de Chagas: influência do sexo dos triatomíneos. Rev Soc Bras Med Trop 24(4):245–250
Okubo A, Maini PK, Williamson MH, Murray JD (1989) On the spatial spread of the grey squirrel in Britain. Proc R Soc Lond Ser B 238(1291):113–125
Pan American Health Organization/World Health Organization (2013) http://www.paho.org/bra/index.php?option=com_content&view=article&id=2541:brasil-dobra-producao-medicamento-contra-doenca-chagas-benzonidazol&Itemid=455
Pan American Health Organization (2014) Resolução CD49.R19: Eliminação de doenças negligenciadas e outras infecções relacionadas à pobreza. http://www.paho.org/bra/index2.php?option=com_docman&task=doc_view&gid=900&Itemid=
Ramirez-Sierra MJ, Herrera-Aguilar M, Gourbire S, Dumonteil E (2010) Patterns of house infestation dynamics by non-domiciliated Triatoma dimidiata reveal a spatial gradient of infestation in rural villages and potential insect manipulation by Trypanosoma cruzi. Trop Med Int Health 15:77–86
Rabinovich JE (1972) Vital statistics of Triatominae (Hemiptera: Reduviidae) under laboratory conditions: I. Triatoma infestans. Klug J Med Ent 9:351–370
Rabinovich JE, Himschoot P (1990) A population-dynamics simulation model of the main vectors of Chagas disease transmission, Rhoudnius prolixus and Triatoma infestans. Ecol Model 52:249–266
Rabinovich JE, Wisnivesky-Colli C, Solarz ND, Gürtler RE (1990) Probability of transmission of Chagas disease by Triatoma infestans (Hemiptera: Reduviidae) in an endemic area of Santiago del Estero, Argentina. Bull World Health Organ 68(6):737–746
Ramsey JM, Townsend PA, Carmona-Castro O, Moo-Llanes DA, Nakazawa Y, Butrick M, Tun-Ku E, de la Cruz-Flix K, Ibarra-Cerdea CN (2015) Atlas of Mexican triatominae (rediviidae: hemiptera) and vector transmission of Chagas disease. Mem Inst Oswaldo Cruz 110(3):339–352
Ribeiro I, Sevcsik A, Alves F, Diap G, Don R, Harhay MO, Chang S, Pecoul B (2009) New, improved treatments for Chagas disease: from the R&D pipeline to the patients. PLoS Negl Trop Dis 3(7):e484
Schofield CJ, Lehane MJ, McEwan P, Catala SS, Gorla DE (1991) Dispersive flight by Triatoma sordida. Trans R Soc Trop Med Hyg 85:676–678
Schofield CJ, Lehane MJ, McEwan P, Catala SS, Gorla DE (1992) Dispersive flight by Triatoma infestans under natural climatic conditions in Argentina. Med Vet Entomol 6:51–56
Silva Sousa A Jr, Cunha Menezes, Palcios VR, Socorro Miranda C, Farias da Costa RJ, Catete CP, Chagasteles EJ, Ribeiro Raithy Pereira AL, Veiga Gonçalves N (2017) Space-temporal analysis of Chagas disease and its environmental and demographic risk factors in the municipality of Barcarena. Pará. Brazil. Rev Bras Epidemiol 20(4):742–755 (in Portuguese)
Slimi R, El Yacoubi S, Dumonteil E, Gourbiere S (2009) A cellular automata model for Chagas disease. Appl Math Model 33:1072–1085
Spagnuolo AM, Shillor M, Stryker GA (2011) A model for Chagas disease with controlled spraying. J Biol Dyn 190:39–69
Spagnuolo AM, Shillor M, Kingsland L, Thatcher A, Toeniskoetter M, Wood B (2012) A logistic delay differential equation model for Chagas disease with interrupted spraying schedules. J Biol Dyn 6(2):377–394
Van den Driessche P, Watmough J (2008) Further notes on the basic reproduction number. In: Mathematical epidemiology, Springer, Berlin, pp 159–178
Velasco-Hernandez JX (1991) An epidemiological model for the dynamics of Chagas disease. BioSyst 26:127–134
Velasco-Hernandez JX (1994) A model for Chagas disease involving transmission by vectors and blood transfusion. Theor Popul Biol 46:1–31
Vianna EN (2011) Dinâmica de reinfestações por triatomíneos e alterações ambientais na ecoepidemiologia da doença de Chagas em área de Triatoma sordida (Hemiptera, Reduviidae, Triatominae) no norte de Minas Gerais, Brasil. PhD thesis. UFMG Instituto de Ciências Biológicas, Minas Gerais
Wisnivesky CC, Gürtler RE, Solarz ND, Schweigmann NJ, Pietrokovsky SM, Alberti A, Flo J (1993) Dispersive flight and house invasion by Triatoma guasayana and Triatoma sordida in Argentina. Mem Inst Oswaldo Cruz 88(1):27–32
Yang HM (2014) The basic reproduction number obtained from jacobian and next generation matrices—a case study of dengue transmission modelling. Biosystem 216:52–75
Yang HM (2017) The transovarial transmission in the dynamic of dengue infection: epidemiological implication and thresholds. Math Biosci 286:1–15
Acknowledgements
We are grateful to the anonymous referees for their comments and suggestions to improve the quality of this paper. The first author acknowledges a grant from CAPES and UFABC.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Vanessa Steindorf: Fellowship CAPES - UFABC.
Rights and permissions
About this article
Cite this article
Steindorf, V., Maidana, N.A. Modeling the Spatial Spread of Chagas Disease. Bull Math Biol 81, 1687–1730 (2019). https://doi.org/10.1007/s11538-019-00581-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-019-00581-5