A metapopulation model for sylvatic  T. cruzi transmission with vector migration

Britnee Crawford; Christopher Kribs-Zaleta

doi:10.3934/mbe.2014.11.471

Article Contents

2014, Volume 11, Issue 3: 471-509. Doi: 10.3934/mbe.2014.11.471

This issue Previous Article The global stability of an SIRS model with infection age Next Article Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population

A metapopulation model for sylvatic T. cruzi transmission with vector migration

Britnee Crawford^1, and
Christopher Kribs-Zaleta^2,

1.
Dallas Baptist University, 3000 Mountain Creek Pkwy, Dallas, TX 75211
2.
UT Arlington Mathematics Dept, Box 19408, Arlington, TX 76019-0408

Received: April 30, 2012

Revised: March 31, 2013

Published: December 2013

Abstract Related Papers Cited by

Abstract

This study presents a metapopulation model for the sylvatic transmission of Trypanosoma cruzi, the etiological agent of Chagas' disease, across multiple geographical regions and multiple overlapping host-vector transmission cycles. Classical qualitative analysis of the model and several submodels focuses on the parasite's basic reproductive number, illustrating how vector migration across patches and multiple transmission routes to hosts (including vertical transmission) determine the infection's persistence in each cycle. Numerical results focus on trends in endemic [equilibrium] persistence levels as functions of vector migration rates, and highlight the significance of the different epidemiological characteristics of transmission in each of the three regions.

Keywords:

Mathematics Subject Classification: Primary: 92D30, 92D40; Secondary: 37N25.

Citation:

Related Papers

Cited by

References

[1]	Y. Benoist, P. Foulon and F. Labourie, Flots d'Anosov a distributions stable et instable differentiables, (French) [Anosov flows with stable and unstable differentiable distributions], J. Amer. Math. Soc., 5 (1992), 33-74.doi: 10.2307/2152750.
[2]	N. Añez and J. S. East, Studies on Trypanosoma rangeli Tejera 1920 II. Its effect on feeding behaviour of triatomine bugs, Acta tropica, 41 (1984), 93-95.
[3]	L. J. Allen, C. L. Wesley, R. D. Owen, D. G. Goodin, D. Koch, C. B. Jonsson, Y. Chu, J. M. Hutchinson and R. L. Paige, A habitat-based model for the spread of hantavirus between reservoir and spillover species, Journal of Theoretical Biology, 260 (2009), 510-522.doi: 10.1016/j.jtbi.2009.07.009.
[4]	J. Arino, J. R. Davis, D. Hartley, R. Jordan, J. M. Miller and P. van den Driessche, A multi-species epidemic model with spatial dynamics, Mathematical Medicine and Biology, 22 (2005), 129-142.doi: 10.1093/imammb/dqi003.
[5]	C. B. Beard, G. Pye, F. J. Steurer, R. Rodriguiz, R. Campman, A. Townsend Peterson, J. Ramsey, R. A. Wirtz and L. E. Robinson, Chagas Disease in a domestic transmission cycle in southern Texas, USA, Emerging Infectious Diseases, 9 (2003), 103-105.doi: 10.3201/eid0901.020217.
[6]	C. Bern and S. P. Montgomery, An estimate of the burden of Chagas disease in the United States, Clinical Infectious Diseases, 49 (2009), 52-54.doi: 10.1086/605091.
[7]	T. W. Box, Density of plains wood rat dens on four plant communities in south Texas, Ecology, 40 (1959), 715-716.
[8]	F. Brauer, C. Castillo-Chavez and J. X. Velasco-Hernández, Recruitment effects in heterosexually transmitted disease models, International Journal of Applied Science and Computation, 3 (1996), 78-90.
[9]	J. K. Braun and M. A. Mares, Neotoma micropus, Mammalian Species, 330 (1989), 1-9.doi: 10.2307/3504233.
[10]	J. E. Burkholder, T. C. Allison and V. P. Kelly, Trypanosoma cruzi (Chagas) (Protozoa: Kinetoplastida) in invertebrate, reservoir, and human hosts of the Lower Rio Grande Valley of Texas, Journal of Parasitology, 66 (1980), 305-311.doi: 10.2307/3280824.
[11]	Centers for Disease Control and Prevention (2012), Chagas Disease, Retrieved from http://www.cdc.gov/parasites/chagas
[12]	A. Cherif, V. Garcia Horton, G. Melendez Rosario and W. Feliciano, A Tale of Two Regions: A Mathematical Model for Chagas' Disease, MTBI Technical Report MTBI 05-05M. Arizona State University 2008.
[13]	C. G. Clark and O. J. Pung, Host specificity of ribosomal DNA variation in sylvatic Trypanosoma cruzi from North America, Molecular and Biochemical Parisitology, 66 (1994), 175-179.
[14]	S. A. Conditt and D. O. Ribble, Social organization of Neotoma micropus, the southern plains woodrat, Am. Midl. Nat., 137 (1996), 290-297.
[15]	B. A. Crawford and C. M. Kribs-Zaleta, Vector migration and dispersal rate for sylvatic T. cruzi transmission, Ecological Complexity, 14 (2013), 145-156.
[16]	S. I. Curto de Casas and R. U. Carcavallo, Climate change and vector-borne diseases distribution, Social Science and Medicine, 40 (1995), 1437-1440.
[17]	P. L. Dorn, C. Monroy and A. Curtis, Triatoma dimidiata (Latreille, 1811): A review of its diversity across its geographic range and the relationship among populations, Infection, Genetics and Evolution, 7 (2007), 343-352.
[18]	R. B. Eads, H. A. Trevino and E. G. Campos, Triatoma (Hemiptera: Reduviidae) Infected with Trypanosoma Cruzi in south Texas wood rat dens, The Southwestern Naturalist, 8 (1963), 38-42.
[19]	E. K. Fritzell and K. J. Haroldson, Urocyon cinereoargenteus, Mammalian Species, 189 (1982), 1-8.doi: 10.2307/3503957.
[20]	S. D. Gehrt and E. K. Fritzell, Duration of familial bonds and dispersal patterns for raccoons in south Texas, J. Mammalogy, 79 (1998), 859-872.doi: 10.2307/1383094.
[21]	S. Gourbiére, E. Dumonteil, J. E. Rabinovich, R. Minkoue and F. Menu, Demographic and dispersal constraints for domestic infestation by non-domicilated Chagas disease vectors in the Yucatan Peninsula, Mexico, American Journal of Tropical Medicine and Hygiene, 78 (2008), 133-139.
[22]	J. M. Gurevitz, L. A. Ceballos, U. Kitron and R. E. Gürtler, Flight initiation of Triatoma Infestans (Hemiptera: Reduviidae) under natural climatic conditions, Journal of Medical Entomology, 43 (2006), 143-150.
[23]	E. J. Hanford, F. B. Zhan, Y. Lu and A. Giordano, Chagas disease in Texas: Recognizing the significance and implications of evidence in the literature, Social Science and Medicine, 65 (2007), 60-79.doi: 10.1016/j.socscimed.2007.02.041.
[24]	M. Harry, F. Lema and C. A. Romaña, Chagas' disease challenge, The Lancet, 355 (2000), 236 pp.doi: 10.1016/S0140-6736(05)72114-0.
[25]	J. O. Ikenga and J. V. Richerson, Trypanosoma cruzi (Chagas) (Protozoa: Kinetoplastida: Trypanosomatidae) in invertebrate and vertebrate hosts from Brewster County in Trans-Pecos Texas, Journal of Economic Entomology, 77 (1984), 126-129.
[26]	S. A. Kjos, K. F. Snowden and J. Olson, Biogeography and Trypanosoma cruzi infection prevalence of Chagas disease vectors in Texas, USA, Vector-Borne and Zoonotic Diseases, 9 (2009), 41-50
[27]	C. Kribs Zaleta, Vector consumption and contact process saturation in sylvatic transmission of T. cruzi, Mathematical Population Studies, 13 (2006), 132-152.doi: 10.1080/08898480600788576.
[28]	C. Kribs Zaleta, Estimating contact process saturation in sylvatic transmission of Trypanosoma cruzi in the U.S., PLOS Neglected Tropical Diseases, 4 (2010), 1-14.
[29]	C. Kribs Zaleta, Alternative transmission modes for Trypanosoma cruzi, Mathematical Bioscences and Engineering, 7 (2010), 657-673.doi: 10.3934/mbe.2010.7.657.
[30]	R. C. Lambert, K. N. Kolivras, L. M. Resler, C. C. Brewster and S. L. Paulson, The potential for emergence of Chagas disease in the United States, Geospatial Health, 2 (2008), 227-239.
[31]	M. J. Lehane, P. K. McEwen, C. J. Whitaker and C. J. Schofield, The role of temperature and nutritional status in flight initiation by Triatoma Infestans, Acta Tropica, 52 (1992), 27-38.
[32]	M. Lewis, J. Renclawowicz and P. van den Driessche, Traveling waves and spread rates for a West Nile virus model, Bulletin of Mathematical Biology, 68 (2006), 3-23.doi: 10.1007/s11538-005-9018-z.
[33]	G. Macdonald, The Epidemiology and Control of Malaria, Oxford: Oxford University Press, 1957.
[34]	N. A. Maidana and H. Mo Yang, Describing the geographic spread of dengue disease by traveling waves, Mathematical Biosciences, 215 (2008), 64-77.doi: 10.1016/j.mbs.2008.05.008.
[35]	K. McBee and R. J. Baker, Dasypus novemcinctus, Mammalian Species, 162 (1982), 1-9.doi: 10.2307/3503864.
[36]	R. Merkelz and S. F. Kerr, Demographics, den use, movements, and absence of Leishmania Mexicana in southern plains woodrats Neotoma micropus, The Southwestern Naturalist, 47 (2002), 70-77.
[37]	J. Milei, R. A. Guerri-Guttenberg, D. Rodolfo Grana and R. Storino, Prognostic impact of Chagas disease in the United States, American Heart Journal, 159 (2009), 22-29.doi: 10.1016/j.ahj.2008.08.024.
[38]	E. Z. Moreno, I. M. Rivera, S. C. Moreno, M. E. Alarcón and A. Lugo-Yarbuh, Vertical transmission of Trypanosoma cruzi in Wistar rats during the acute phase of infection, Investigación clínica (Maracaibo), 44 (2003).
[39]	J. D.Murray, E. A. Stanely and D. L. Brown, On the spatial spread of rabies among foxes, Precedings of the Royal Society of London, 229 (1986), 111-1150.
[40]	S. M. Pietzrak and O. J. Pung, Trypanosomiasis in raccoons from Georgia, Journal of Wildlife Diseases, 34 (1998), 132-136.
[41]	W. F. Pippin, The biology and vector capability of Triatoma Sanguisuga Texana Usinger and Triatoma Gerstaeckeri (Stål)(Hemiptera: Triatominae), Journal of Medical Entomology, 7 (1970), 30-45.
[42]	O. J. Pung, C. W. Banks, D. N. Jones and M. W. Krissinger, Trypanosoma cruzi in wild raccoons, opossums, and triatomine bugs in southeast Georgia, USA, Journal of Parasitology, 81 (1995), 583-587.
[43]	G. G. Raun, A population of woodrats (Neotoma micropus) in southwest Texas, Bull. Texas Mem. Mus., 11 (1966), 1-62.
[44]	R. W. Raymond, C. P. McHugh, L. R. Witt and S. F. Kerr, Temporal and spatial distribution of Leishmania mexicana infections in a population of Neotoma micropus, Mem. Inst. Oswaldo Cruz., 98 (2003), 171-180.
[45]	D. M. Roellig, E. L. Brown, C. Barnabé, M. Tibayrenc, F. J. Steurer and M. J. Yabsley, Molecular typing of Trypanosoma cruzi isolates, United States, Emerging Infectious Diseases, 14 (2008), 1123-1125.
[46]	R. Ross, The Prevention of Malaria, (2nd edition). London: Murray 1911.
[47]	S. Sarkar, S. E. Strutz, D. M. Frank, C. L. Rivaldi, B. Sissel and V. Sánchez-Cordero, Chagas disease risk in Texas, PLoS Neglected Tropical Diseases, 4 (2010), 1-14.doi: 10.1371/journal.pntd.0000836.
[48]	C. J. Schofield, M. J. Lehane, P. McEwen, S. S. Catala and D. E. Gorla, Dispersive flight by Triatoma Infestans under natural climatic conditions in Argentina, Medical and Veterinary Entomology, 6 (1992), 51-56.
[49]	H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, Journal of Mathematical Biology, 30 (1992), 755-763.doi: 10.1007/BF00173267.
[50]	H. R. Thieme, Asymptotically autonomous differential equations in the plane, Rocky Mountain Journal of Mathematics, 24 (1994), 351-380.doi: 10.1216/rmjm/1181072470.
[51]	K. M. Thies, M. L. Thies and W. Caire, House construction by the southern plains woodrat (Neotoma micropus) in southwestern Oklahoma, The Southwestern Naturalist, 41 (1996), 116-122.
[52]	M. L. Thies and W. Caire, Nearest-neighbor analysis of the spatial distribution of houses Neotoma micropus in southwestern Oklahoma, The Southwestern Naturalist, 36 (1991), 233-262.
[53]	P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.doi: 10.1016/S0025-5564(02)00108-6.
[54]	J. X. Velasco-Hernández, An epidemiological model for the dynamics of Chagas' disease, Biosystems, 26 (1991), 127-134.doi: 10.1016/0303-2647(91)90043-K.
[55]	M. E. Villagrán, C. Marin, A. Hurtado, M. Sánchez-Moreno and J. Antonio de Diego, Natural infection and distribution of Triatomines (Hemiptera: Reduviidae) in the state of Querétaro, Mexico, The Royal Society of Tropical Medicine and Hygiene, 102 (2008), 833-838.
[56]	J. Wade-Smith and B. J. Verts, Mephitis mephitis, Mammalian Species, 173 (1982), 1-7.
[57]	World Health Organization (2010), Chagas Disease: American Trypanosomiasis, Retrieved from http://www.who.int/mediacentre/factsheets/fs340/en
[58]	M. Yabsley and G. Pittman Noblet, Biological and molecular characterization of a raccoon isolate of Trypanosoma cruzi from South Carolina, Journal of Parasitology, 88 (2002), 1273-1276.
[59]	M. Yabsley, J. Barnes, A. Ellis, S. Kjos and C. Roxanne, Southern plains woodrats (Neotoma micropus) from southern Texas are important reservoirs of two genotypes of Trypanosoma cruzi and a host of a putative novel Trypanosoma species, Vector-Borne and Zoonotic Diseases, 13 (2012), 1-9.
[60]	R. Zeledón, and J. E. Rabinovich, Chagas' Disease: An ecological appraisal with special emphasis on its insect vectors, Annual Review of Entomology, 26 (1981), 101-133.
[61]	B. Zingales, S. G. Andrade, M. Briones, D. A. Campbell, E. Chiari, O. Fernandes, F. Guhl, E Lages-Silva, A. Macedo, C. R. Machado, M. A. Miles, A. J. Romanha, N. R. Sturm, M. Tibayrenc and A. G. Schijman, A new consensus for Trypanosoma cruzi intraspecific nomenclature: Second revision meeting recommends TcI to TcVI, Mem. Inst. Oswaldo Cruz., 104 (2009), 1051-1054.