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Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment
1. | Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada, Canada |
2. | Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 |
References:
[1] |
Best Country Report, Temperature map of Canada. Available from: http://www.bestcountryreports.com/Temperature_Map_Canada.html [Accessed date: 24 February, 2011]. |
[2] |
L. Bourouiba, J. Wu, S. Newman, J. Takekawa and T. Natdorj, et al., Spatial dynamics of bar-headed geese migration in the context of H5N1, J. R. Soc. Interface, 7 (2010), 1627-1639. |
[3] |
R. Breban, J. M. Drake, D. E. Stallknecht and P. Rohani, The role of environmental transmission in recurrent avian influenza epidemics, PLoS Comput. Biol., 5 (2009), e1000346. |
[4] |
J. D. Brown, G. Goekjian, R. Poulson, S. Valeika and D. E. Stallknecht, Avian influenza virus in water: Infectivity is dependent on pH, salinity and temperature, Vet. Microbiol., 136 (2009), 20-26. |
[5] |
J. D. Brown, D. E. Swayne, R. J. Cooper, R. E. Burns and D. E. Stallknecht, Persistence of H5 and H7 avian influenza viruses in water, Avian. Dis., 51 (2007), 285-289. |
[6] |
I. Davidson, S. Nagar, R. Haddas, M. Ben-Shabat and N. Golender, et al., Avian influenza virus H9N2 survival at different temperatures and pHs, Avian. Dis., 54 (2010), 725-728.
doi: 10.1637/8736-032509-ResNote.1. |
[7] |
K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, Berlin, 1985. |
[8] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproductionratio $R_0$ in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[9] |
R. A. Fouchier, V. Munster, A. Wallensten, T. M. Bestebroer and S. Herfst, et al., Characterization of a novel influenza A virus hemagglutinin subtype (H16) obtained from black-headed gulls, J. Virol., 79 (2005), 2814-2822. |
[10] |
V. Henaux, M. D. Samuel and C. M. Bunck, Model-based evaluation of highly and low pathogenic avian influenza dynamics in wild birds, PLoS One, 5 (2010), e10997. |
[11] |
P. Hess, "Periodic-parabolic Boundary Value Problem and Positivity," Pitman Res. Notes Math., 247, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
[12] |
V. S. Hinshaw, R. G. Webster and B. Turner, The perpetuation of orthomyxoviruses and paramyxoviruses in Canadian waterfowl, Can.J. Microbiol., 26 (1980), 622-629.
doi: 10.1139/m80-108. |
[13] |
V. S. Hinshaw, R. G. Webster and B. Turner, Water-bone transmission of influenza A viruses?, Intervirology, 11 (1979), 66-68.
doi: 10.1159/000149014. |
[14] |
S.-B. Hsu, J. Jiang, and F.-B. Wang, On a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat, J. Diff. Eqns., 248 (2010), 2470-2496.
doi: 10.1016/j.jde.2009.12.014. |
[15] |
S.-B. Hsu, F. B. Wang and X.-Q. Zhao, Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, to appear in Journal of Dynamics and Differential Equations. |
[16] |
J. Jiang, X. Liang and X.-Q. Zhao, Saddle point behavior for monotone semiflows and reaction-diffusion models, J. Diff. Eqns., 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[17] |
S. Krauss, D. Walker, S. P. Pryor, L. Niles and L. Chenghong, et al., Influenza A viruses of migrating wild aquatic birds in North America, Vector Borne Zoonotic Dis., 4 (2004), 177-189. |
[18] |
Y. Lou and X.-Q. Zhao, A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62 (2011), 543-568.
doi: 10.1007/s00285-010-0346-8. |
[19] |
H. Lu and A. E. Castro, Evaluation of the infectivity, length of infection, and immune response of a low-pathogenicity H7N2 avian influenza virus in specific-pathogen-free chickens, Avian. Dis., 48 (2004), 263-270.
doi: 10.1637/7064. |
[20] |
R. H. Martin and H. L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. of A. M. S., 321 (1990), 1-44. |
[21] |
P. Magal and X. -Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[22] |
B. Olsen, V. J. Munster, A. Wallensten, J. Waldenstrom and A. D. Osterhaus, et al., Global patterns of influenza a virus in wild birds, Science, 312, 384-388. |
[23] |
B. Roche, C. Lebarbenchon, M. Gauthier-Clerc, C. M. Chang and F. Thomas, et al., Water-borne transmission drives avian influenza dynamics in wild birds: The case of the 2005-2006 epidemics in the Camargue area, Infect. Genet. Evol., 9 (2009), 800-805. |
[24] |
P. Rohani, R. Breban, D. E. Stallknecht and J. M. Drake, Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion, Proc. Natl. Acad. Sci. USA, 106 (2009), 10365-10369.
doi: 10.1073/pnas.0809026106. |
[25] |
M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," Corrected reprint of the 1967 original, Springer-Verlag, New York, 1984. |
[26] |
H. L. Smith, "Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems," Math. Surveys Monogr., 41, American Mathematical Society, Providence, RI, 1995. |
[27] |
H. L. Smith and X.-Q. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[28] |
D. E. Stallknecht, S. M. Shane, M. T. Kearney and P. J. Zwank, Persistence of avian influenza viruses in water, Avian. Dis., 34 (1990), 406-411.
doi: 10.2307/1591428. |
[29] |
J. H. Tien and D. J. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bull. Math. Biol., 72 (2010), 1506-1533.
doi: 10.1007/s11538-010-9507-6. |
[30] |
H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
doi: 10.1007/BF00173267. |
[31] |
H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211. |
[32] |
N. K. Vaidya and L. M. Wahl, The sensitivity of avian influenza dynamics in wild birds to time-varying environmental temperature, (2011), submitted. |
[33] |
P. van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[34] |
F.-B. Wang, A system of partial differential equations modeling the competition for two complementary resources in flowing habitats, J. Diff. Eqns., 249 (2010), 2866-2888.
doi: 10.1016/j.jde.2010.07.031. |
[35] |
W. Wang and X.-Q. Zhao, A nonlocal and time-delayed reaction-diffusion model of dengue transmission, SIAM J. Appl. Math., 71 (2011), 147-168.
doi: 10.1137/090775890. |
[36] |
R. G. Webster, W. J. Bean, O. T. Gorman, T. M. Chambers and Y. Kawaoka, Evolution and ecology of influenza A viruses, Microbiol. Rev., 56 (1992), 152-179. |
[37] |
R. G. Webster, M. Yakhno, V. S. Hinshaw, W. J. Bean and K. G. Murti, Intestinal influenza: Replication and characterization of influenza viruses in ducks, Virology, 84 (1978), 268-278.
doi: 10.1016/0042-6822(78)90247-7. |
[38] |
K. F. Zhang and X.-Q. Zhao, Asymptotic behaviour of a reaction-diffusionmodel with a quiescent stage, Proc. R. Soc. Lond. Ser. A. Math. Phys. Eng. Sci., 463 (2007), 1029-1043.
doi: 10.1098/rspa.2006.1806. |
show all references
References:
[1] |
Best Country Report, Temperature map of Canada. Available from: http://www.bestcountryreports.com/Temperature_Map_Canada.html [Accessed date: 24 February, 2011]. |
[2] |
L. Bourouiba, J. Wu, S. Newman, J. Takekawa and T. Natdorj, et al., Spatial dynamics of bar-headed geese migration in the context of H5N1, J. R. Soc. Interface, 7 (2010), 1627-1639. |
[3] |
R. Breban, J. M. Drake, D. E. Stallknecht and P. Rohani, The role of environmental transmission in recurrent avian influenza epidemics, PLoS Comput. Biol., 5 (2009), e1000346. |
[4] |
J. D. Brown, G. Goekjian, R. Poulson, S. Valeika and D. E. Stallknecht, Avian influenza virus in water: Infectivity is dependent on pH, salinity and temperature, Vet. Microbiol., 136 (2009), 20-26. |
[5] |
J. D. Brown, D. E. Swayne, R. J. Cooper, R. E. Burns and D. E. Stallknecht, Persistence of H5 and H7 avian influenza viruses in water, Avian. Dis., 51 (2007), 285-289. |
[6] |
I. Davidson, S. Nagar, R. Haddas, M. Ben-Shabat and N. Golender, et al., Avian influenza virus H9N2 survival at different temperatures and pHs, Avian. Dis., 54 (2010), 725-728.
doi: 10.1637/8736-032509-ResNote.1. |
[7] |
K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, Berlin, 1985. |
[8] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproductionratio $R_0$ in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[9] |
R. A. Fouchier, V. Munster, A. Wallensten, T. M. Bestebroer and S. Herfst, et al., Characterization of a novel influenza A virus hemagglutinin subtype (H16) obtained from black-headed gulls, J. Virol., 79 (2005), 2814-2822. |
[10] |
V. Henaux, M. D. Samuel and C. M. Bunck, Model-based evaluation of highly and low pathogenic avian influenza dynamics in wild birds, PLoS One, 5 (2010), e10997. |
[11] |
P. Hess, "Periodic-parabolic Boundary Value Problem and Positivity," Pitman Res. Notes Math., 247, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1991. |
[12] |
V. S. Hinshaw, R. G. Webster and B. Turner, The perpetuation of orthomyxoviruses and paramyxoviruses in Canadian waterfowl, Can.J. Microbiol., 26 (1980), 622-629.
doi: 10.1139/m80-108. |
[13] |
V. S. Hinshaw, R. G. Webster and B. Turner, Water-bone transmission of influenza A viruses?, Intervirology, 11 (1979), 66-68.
doi: 10.1159/000149014. |
[14] |
S.-B. Hsu, J. Jiang, and F.-B. Wang, On a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat, J. Diff. Eqns., 248 (2010), 2470-2496.
doi: 10.1016/j.jde.2009.12.014. |
[15] |
S.-B. Hsu, F. B. Wang and X.-Q. Zhao, Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, to appear in Journal of Dynamics and Differential Equations. |
[16] |
J. Jiang, X. Liang and X.-Q. Zhao, Saddle point behavior for monotone semiflows and reaction-diffusion models, J. Diff. Eqns., 203 (2004), 313-330.
doi: 10.1016/j.jde.2004.05.002. |
[17] |
S. Krauss, D. Walker, S. P. Pryor, L. Niles and L. Chenghong, et al., Influenza A viruses of migrating wild aquatic birds in North America, Vector Borne Zoonotic Dis., 4 (2004), 177-189. |
[18] |
Y. Lou and X.-Q. Zhao, A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62 (2011), 543-568.
doi: 10.1007/s00285-010-0346-8. |
[19] |
H. Lu and A. E. Castro, Evaluation of the infectivity, length of infection, and immune response of a low-pathogenicity H7N2 avian influenza virus in specific-pathogen-free chickens, Avian. Dis., 48 (2004), 263-270.
doi: 10.1637/7064. |
[20] |
R. H. Martin and H. L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. of A. M. S., 321 (1990), 1-44. |
[21] |
P. Magal and X. -Q. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM. J. Math. Anal., 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[22] |
B. Olsen, V. J. Munster, A. Wallensten, J. Waldenstrom and A. D. Osterhaus, et al., Global patterns of influenza a virus in wild birds, Science, 312, 384-388. |
[23] |
B. Roche, C. Lebarbenchon, M. Gauthier-Clerc, C. M. Chang and F. Thomas, et al., Water-borne transmission drives avian influenza dynamics in wild birds: The case of the 2005-2006 epidemics in the Camargue area, Infect. Genet. Evol., 9 (2009), 800-805. |
[24] |
P. Rohani, R. Breban, D. E. Stallknecht and J. M. Drake, Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion, Proc. Natl. Acad. Sci. USA, 106 (2009), 10365-10369.
doi: 10.1073/pnas.0809026106. |
[25] |
M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations," Corrected reprint of the 1967 original, Springer-Verlag, New York, 1984. |
[26] |
H. L. Smith, "Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems," Math. Surveys Monogr., 41, American Mathematical Society, Providence, RI, 1995. |
[27] |
H. L. Smith and X.-Q. Zhao, Robust persistence for semidynamical systems, Nonlinear Anal., 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[28] |
D. E. Stallknecht, S. M. Shane, M. T. Kearney and P. J. Zwank, Persistence of avian influenza viruses in water, Avian. Dis., 34 (1990), 406-411.
doi: 10.2307/1591428. |
[29] |
J. H. Tien and D. J. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bull. Math. Biol., 72 (2010), 1506-1533.
doi: 10.1007/s11538-010-9507-6. |
[30] |
H. R. Thieme, Convergence results and a Poincare-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992), 755-763.
doi: 10.1007/BF00173267. |
[31] |
H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188-211. |
[32] |
N. K. Vaidya and L. M. Wahl, The sensitivity of avian influenza dynamics in wild birds to time-varying environmental temperature, (2011), submitted. |
[33] |
P. van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[34] |
F.-B. Wang, A system of partial differential equations modeling the competition for two complementary resources in flowing habitats, J. Diff. Eqns., 249 (2010), 2866-2888.
doi: 10.1016/j.jde.2010.07.031. |
[35] |
W. Wang and X.-Q. Zhao, A nonlocal and time-delayed reaction-diffusion model of dengue transmission, SIAM J. Appl. Math., 71 (2011), 147-168.
doi: 10.1137/090775890. |
[36] |
R. G. Webster, W. J. Bean, O. T. Gorman, T. M. Chambers and Y. Kawaoka, Evolution and ecology of influenza A viruses, Microbiol. Rev., 56 (1992), 152-179. |
[37] |
R. G. Webster, M. Yakhno, V. S. Hinshaw, W. J. Bean and K. G. Murti, Intestinal influenza: Replication and characterization of influenza viruses in ducks, Virology, 84 (1978), 268-278.
doi: 10.1016/0042-6822(78)90247-7. |
[38] |
K. F. Zhang and X.-Q. Zhao, Asymptotic behaviour of a reaction-diffusionmodel with a quiescent stage, Proc. R. Soc. Lond. Ser. A. Math. Phys. Eng. Sci., 463 (2007), 1029-1043.
doi: 10.1098/rspa.2006.1806. |
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