2014, 11(3): 471-509. doi: 10.3934/mbe.2014.11.471

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

1. 

Dallas Baptist University, 3000 Mountain Creek Pkwy, Dallas, TX 75211, United States

2. 

UT Arlington Mathematics Dept, Box 19408, Arlington, TX 76019-0408, United States

Received  May 2012 Revised  April 2013 Published  January 2014

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.
Citation: Britnee Crawford, Christopher Kribs-Zaleta. A metapopulation model for sylvatic T. cruzi transmission with vector migration. Mathematical Biosciences & Engineering, 2014, 11 (3) : 471-509. doi: 10.3934/mbe.2014.11.471
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], 5 (1992), 33. doi: 10.2307/2152750. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.jtbi.2009.07.009. Google Scholar

[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. doi: 10.1093/imammb/dqi003. Google Scholar

[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. doi: 10.3201/eid0901.020217. Google Scholar

[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. doi: 10.1086/605091. Google Scholar

[7]

T. W. Box, Density of plains wood rat dens on four plant communities in south Texas,, Ecology, 40 (1959), 715. Google Scholar

[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. Google Scholar

[9]

J. K. Braun and M. A. Mares, Neotoma micropus,, Mammalian Species, 330 (1989), 1. doi: 10.2307/3504233. Google Scholar

[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. doi: 10.2307/3280824. Google Scholar

[11]

Centers for Disease Control and Prevention (2012), Chagas Disease,, Retrieved from , (). Google Scholar

[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., (2008), 05. Google Scholar

[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. Google Scholar

[14]

S. A. Conditt and D. O. Ribble, Social organization of Neotoma micropus, the southern plains woodrat,, Am. Midl. Nat., 137 (1996), 290. Google Scholar

[15]

B. A. Crawford and C. M. Kribs-Zaleta, Vector migration and dispersal rate for sylvatic T. cruzi transmission,, Ecological Complexity, 14 (2013), 145. Google Scholar

[16]

S. I. Curto de Casas and R. U. Carcavallo, Climate change and vector-borne diseases distribution,, Social Science and Medicine, 40 (1995), 1437. Google Scholar

[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, 7 (2007), 343. Google Scholar

[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. Google Scholar

[19]

E. K. Fritzell and K. J. Haroldson, Urocyon cinereoargenteus,, Mammalian Species, 189 (1982), 1. doi: 10.2307/3503957. Google Scholar

[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. doi: 10.2307/1383094. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.socscimed.2007.02.041. Google Scholar

[24]

M. Harry, F. Lema and C. A. Romaña, Chagas' disease challenge,, The Lancet, 355 (2000). doi: 10.1016/S0140-6736(05)72114-0. Google Scholar

[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. Google Scholar

[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. Google Scholar

[27]

C. Kribs Zaleta, Vector consumption and contact process saturation in sylvatic transmission of T. cruzi,, Mathematical Population Studies, 13 (2006), 132. doi: 10.1080/08898480600788576. Google Scholar

[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. Google Scholar

[29]

C. Kribs Zaleta, Alternative transmission modes for Trypanosoma cruzi,, Mathematical Bioscences and Engineering, 7 (2010), 657. doi: 10.3934/mbe.2010.7.657. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1007/s11538-005-9018-z. Google Scholar

[33]

G. Macdonald, The Epidemiology and Control of Malaria,, Oxford: Oxford University Press, (1957). Google Scholar

[34]

N. A. Maidana and H. Mo Yang, Describing the geographic spread of dengue disease by traveling waves,, Mathematical Biosciences, 215 (2008), 64. doi: 10.1016/j.mbs.2008.05.008. Google Scholar

[35]

K. McBee and R. J. Baker, Dasypus novemcinctus,, Mammalian Species, 162 (1982), 1. doi: 10.2307/3503864. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.ahj.2008.08.024. Google Scholar

[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). Google Scholar

[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. Google Scholar

[40]

S. M. Pietzrak and O. J. Pung, Trypanosomiasis in raccoons from Georgia,, Journal of Wildlife Diseases, 34 (1998), 132. Google Scholar

[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. Google Scholar

[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. Google Scholar

[43]

G. G. Raun, A population of woodrats (Neotoma micropus) in southwest Texas,, Bull. Texas Mem. Mus., 11 (1966), 1. Google Scholar

[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. Google Scholar

[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. Google Scholar

[46]

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[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. doi: 10.1371/journal.pntd.0000836. Google Scholar

[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. Google Scholar

[49]

H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations,, Journal of Mathematical Biology, 30 (1992), 755. doi: 10.1007/BF00173267. Google Scholar

[50]

H. R. Thieme, Asymptotically autonomous differential equations in the plane,, Rocky Mountain Journal of Mathematics, 24 (1994), 351. doi: 10.1216/rmjm/1181072470. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar

[54]

J. X. Velasco-Hernández, An epidemiological model for the dynamics of Chagas' disease,, Biosystems, 26 (1991), 127. doi: 10.1016/0303-2647(91)90043-K. Google Scholar

[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. Google Scholar

[56]

J. Wade-Smith and B. J. Verts, Mephitis mephitis, Mammalian Species,, 173 (1982), 173 (1982), 1. Google Scholar

[57]

World Health Organization (2010), Chagas Disease: American Trypanosomiasis,, Retrieved from , (). Google Scholar

[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. Google Scholar

[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. Google Scholar

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show all references

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], 5 (1992), 33. doi: 10.2307/2152750. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.jtbi.2009.07.009. Google Scholar

[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. doi: 10.1093/imammb/dqi003. Google Scholar

[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. doi: 10.3201/eid0901.020217. Google Scholar

[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. doi: 10.1086/605091. Google Scholar

[7]

T. W. Box, Density of plains wood rat dens on four plant communities in south Texas,, Ecology, 40 (1959), 715. Google Scholar

[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. Google Scholar

[9]

J. K. Braun and M. A. Mares, Neotoma micropus,, Mammalian Species, 330 (1989), 1. doi: 10.2307/3504233. Google Scholar

[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. doi: 10.2307/3280824. Google Scholar

[11]

Centers for Disease Control and Prevention (2012), Chagas Disease,, Retrieved from , (). Google Scholar

[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., (2008), 05. Google Scholar

[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. Google Scholar

[14]

S. A. Conditt and D. O. Ribble, Social organization of Neotoma micropus, the southern plains woodrat,, Am. Midl. Nat., 137 (1996), 290. Google Scholar

[15]

B. A. Crawford and C. M. Kribs-Zaleta, Vector migration and dispersal rate for sylvatic T. cruzi transmission,, Ecological Complexity, 14 (2013), 145. Google Scholar

[16]

S. I. Curto de Casas and R. U. Carcavallo, Climate change and vector-borne diseases distribution,, Social Science and Medicine, 40 (1995), 1437. Google Scholar

[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, 7 (2007), 343. Google Scholar

[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. Google Scholar

[19]

E. K. Fritzell and K. J. Haroldson, Urocyon cinereoargenteus,, Mammalian Species, 189 (1982), 1. doi: 10.2307/3503957. Google Scholar

[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. doi: 10.2307/1383094. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.socscimed.2007.02.041. Google Scholar

[24]

M. Harry, F. Lema and C. A. Romaña, Chagas' disease challenge,, The Lancet, 355 (2000). doi: 10.1016/S0140-6736(05)72114-0. Google Scholar

[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. Google Scholar

[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. Google Scholar

[27]

C. Kribs Zaleta, Vector consumption and contact process saturation in sylvatic transmission of T. cruzi,, Mathematical Population Studies, 13 (2006), 132. doi: 10.1080/08898480600788576. Google Scholar

[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. Google Scholar

[29]

C. Kribs Zaleta, Alternative transmission modes for Trypanosoma cruzi,, Mathematical Bioscences and Engineering, 7 (2010), 657. doi: 10.3934/mbe.2010.7.657. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1007/s11538-005-9018-z. Google Scholar

[33]

G. Macdonald, The Epidemiology and Control of Malaria,, Oxford: Oxford University Press, (1957). Google Scholar

[34]

N. A. Maidana and H. Mo Yang, Describing the geographic spread of dengue disease by traveling waves,, Mathematical Biosciences, 215 (2008), 64. doi: 10.1016/j.mbs.2008.05.008. Google Scholar

[35]

K. McBee and R. J. Baker, Dasypus novemcinctus,, Mammalian Species, 162 (1982), 1. doi: 10.2307/3503864. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/j.ahj.2008.08.024. Google Scholar

[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). Google Scholar

[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. Google Scholar

[40]

S. M. Pietzrak and O. J. Pung, Trypanosomiasis in raccoons from Georgia,, Journal of Wildlife Diseases, 34 (1998), 132. Google Scholar

[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. Google Scholar

[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. Google Scholar

[43]

G. G. Raun, A population of woodrats (Neotoma micropus) in southwest Texas,, Bull. Texas Mem. Mus., 11 (1966), 1. Google Scholar

[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. Google Scholar

[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. Google Scholar

[46]

R. Ross, The Prevention of Malaria,, (2nd edition). London: Murray 1911., (1911). Google Scholar

[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. doi: 10.1371/journal.pntd.0000836. Google Scholar

[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. Google Scholar

[49]

H. R. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations,, Journal of Mathematical Biology, 30 (1992), 755. doi: 10.1007/BF00173267. Google Scholar

[50]

H. R. Thieme, Asymptotically autonomous differential equations in the plane,, Rocky Mountain Journal of Mathematics, 24 (1994), 351. doi: 10.1216/rmjm/1181072470. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. doi: 10.1016/S0025-5564(02)00108-6. Google Scholar

[54]

J. X. Velasco-Hernández, An epidemiological model for the dynamics of Chagas' disease,, Biosystems, 26 (1991), 127. doi: 10.1016/0303-2647(91)90043-K. Google Scholar

[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. Google Scholar

[56]

J. Wade-Smith and B. J. Verts, Mephitis mephitis, Mammalian Species,, 173 (1982), 173 (1982), 1. Google Scholar

[57]

World Health Organization (2010), Chagas Disease: American Trypanosomiasis,, Retrieved from , (). Google Scholar

[58]

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