2016, 13(2): 401-424. doi: 10.3934/mbe.2015009

A mathematical model for the spread of west nile virus in migratory and resident birds

1. 

Department of Mathematics, Tulane University, New Orleans, LA 70118, United States, United States, United States

Received  January 2015 Revised  November 2015 Published  December 2015

We develop a mathematical model for transmission of West Nile virus (WNV) that incorporates resident and migratory host avian populations and a mosquito vector population. We provide a detailed analysis of the model's basic reproductive number and demonstrate how the exposed infected, but not infectious, state for the bird population can be approximated by a reduced model. We use the model to investigate the interplay of WNV in both resident and migratory bird hosts. The resident host parameters correspond to the American Crow (Corvus brachyrhynchos), a competent host with a high death rate due to disease, and migratory host parameters to the American Robin (Turdus migratorius), a competent host with low WNV death rates. We find that yearly seasonal outbreaks depend primarily on the number of susceptible migrant birds entering the local population each season. We observe that the early growth rates of seasonal outbreaks is more influenced by the the migratory population than the resident bird population. This implies that although the death of highly competent resident birds, such as American Crows, are good indicators for the presence of the virus, these species have less impact on the basic reproductive number than the competent migratory birds with low death rates, such as the American Robins. The disease forecasts are most sensitive to the assumptions about the feeding preferences of North American mosquito vectors and the effect of the virus on the hosts. Increased research on the these factors would allow for better estimates of these important model parameters, which would improve the quality of future WNV forecasts.
Citation: Louis D. Bergsman, James M. Hyman, Carrie A. Manore. A mathematical model for the spread of west nile virus in migratory and resident birds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 401-424. doi: 10.3934/mbe.2015009
References:
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L. M. Arriola and J. M. Hyman, Being sensitive to uncertainty,, Computing in Science & Engineering, 9 (2007), 10.  doi: 10.1109/MCSE.2007.27.  Google Scholar

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T. A. Beveroth, M. P. Ward, R. L. Lampman, A. M. Ringia and R. J. Novak, Changes in seroprevalence of west nile virus across illinois in free-ranging birds from 2001 through 2004,, The American journal of tropical medicine and hygiene, 74 (2006), 174.   Google Scholar

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D. B. Botkin and R. S. Miller, Mortality rates and survival of birds,, American Naturalist, 108 (1974), 181.  doi: 10.1086/282898.  Google Scholar

[6]

C. Bowman, A. Gumel, P. Van den Driessche, J. Wu and H. Zhu, A mathematical model for assessing control strategies against west nile virus,, Bulletin of mathematical biology, 67 (2005), 1107.  doi: 10.1016/j.bulm.2005.01.002.  Google Scholar

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C. A. Bradley, S. E. J. Gibbs and S. Altizer, Urban land use predicts west nile virus exposure in songbirds,, Ecological Applications, 18 (2008), 1083.  doi: 10.1890/07-0822.1.  Google Scholar

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S. Chatterjee, S. Pal and J. Chattopadhyay, Role of migratory birds under environmental fluctuation: a mathematical study,, Journal of Biological Systems, 16 (2008), 81.  doi: 10.1142/S0218339008002423.  Google Scholar

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N. Chitnis, J. Cushing and J. Hyman, Bifurcation analysis of a mathematical model for malaria transmission,, SIAM Journal on Applied Mathematics, 67 (2006), 24.  doi: 10.1137/050638941.  Google Scholar

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N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model,, Bulletin of mathematical biology, 70 (2008), 1272.  doi: 10.1007/s11538-008-9299-0.  Google Scholar

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L. Colton, B. J. Biggerstaff, A. Johnson and R. S. Nasci, Quantification of west nile virus in vector mosquito saliva,, Journal of the American Mosquito Control Association, 21 (2005), 49.   Google Scholar

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G. Cruz-Pacheco, L. Esteva, J. Montaø-Hirose and C. Vargas, Modelling the dynamics of west nile virus,, Bulletin of mathematical biology, 67 (2005), 1157.  doi: 10.1016/j.bulm.2004.11.008.  Google Scholar

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G. Cruz-Pacheco, L. Esteva and C. Vargas, Multi-species interactions in west nile virus infection,, Journal of Biological Dynamics, 6 (2012), 281.  doi: 10.1080/17513758.2011.571721.  Google Scholar

[16]

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[27]

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[28]

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C. A. Manore, K. S. Hickmann, S. Xu, H. J. Wearing and J. M. Hyman, Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus,, Journal of theoretical biology, 356 (2014), 174.  doi: 10.1016/j.jtbi.2014.04.033.  Google Scholar

[31]

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[32]

S. Moore, C. Manore, V. Bokil, E. Borer and P. Hosseini, Spatiotemporal model of barley and cereal yellow dwarf virus transmission dynamics with seasonality and plant competition,, Bulletin of Mathematical Biology, 73 (2011), 2707.  doi: 10.1007/s11538-011-9654-4.  Google Scholar

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[40]

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[41]

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show all references

References:
[1]

A. Abdelrazec, S. Lenhart and H. Zhu, Transmission dynamics of west nile virus in mosquitoes and corvids and non-corvids,, Journal of mathematical biology, 68 (2014), 1553.  doi: 10.1007/s00285-013-0677-3.  Google Scholar

[2]

L. Arriola and J. M. Hyman, Sensitivity analysis for uncertainty quantification in mathematical models,, in Mathematical and Statistical Estimation Approaches in Epidemiology, (2009), 195.  doi: 10.1007/978-90-481-2313-1_10.  Google Scholar

[3]

L. M. Arriola and J. M. Hyman, Being sensitive to uncertainty,, Computing in Science & Engineering, 9 (2007), 10.  doi: 10.1109/MCSE.2007.27.  Google Scholar

[4]

T. A. Beveroth, M. P. Ward, R. L. Lampman, A. M. Ringia and R. J. Novak, Changes in seroprevalence of west nile virus across illinois in free-ranging birds from 2001 through 2004,, The American journal of tropical medicine and hygiene, 74 (2006), 174.   Google Scholar

[5]

D. B. Botkin and R. S. Miller, Mortality rates and survival of birds,, American Naturalist, 108 (1974), 181.  doi: 10.1086/282898.  Google Scholar

[6]

C. Bowman, A. Gumel, P. Van den Driessche, J. Wu and H. Zhu, A mathematical model for assessing control strategies against west nile virus,, Bulletin of mathematical biology, 67 (2005), 1107.  doi: 10.1016/j.bulm.2005.01.002.  Google Scholar

[7]

C. A. Bradley, S. E. J. Gibbs and S. Altizer, Urban land use predicts west nile virus exposure in songbirds,, Ecological Applications, 18 (2008), 1083.  doi: 10.1890/07-0822.1.  Google Scholar

[8]

S. Chatterjee, S. Pal and J. Chattopadhyay, Role of migratory birds under environmental fluctuation: a mathematical study,, Journal of Biological Systems, 16 (2008), 81.  doi: 10.1142/S0218339008002423.  Google Scholar

[9]

N. Chitnis, J. Cushing and J. Hyman, Bifurcation analysis of a mathematical model for malaria transmission,, SIAM Journal on Applied Mathematics, 67 (2006), 24.  doi: 10.1137/050638941.  Google Scholar

[10]

N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model,, Bulletin of mathematical biology, 70 (2008), 1272.  doi: 10.1007/s11538-008-9299-0.  Google Scholar

[11]

N. Chitnis, J. M. Hyman and C. A. Manore, Modelling vertical transmission in vector-borne diseases with applications to Rift Valley fever,, Journal of Biological Dynamics, 7 (2013), 11.  doi: 10.1080/17513758.2012.733427.  Google Scholar

[12]

D. Chowell-Puente, P. Delgado, D. Pérez, C. H. S. Tapia, F. Sánchez and D. Murillo, The Impact of Mosquito-Bird Interaction on the Spread of West Nile Virus to Human Populations,, Department of Biometrics, ().   Google Scholar

[13]

L. Colton, B. J. Biggerstaff, A. Johnson and R. S. Nasci, Quantification of west nile virus in vector mosquito saliva,, Journal of the American Mosquito Control Association, 21 (2005), 49.   Google Scholar

[14]

G. Cruz-Pacheco, L. Esteva, J. Montaø-Hirose and C. Vargas, Modelling the dynamics of west nile virus,, Bulletin of mathematical biology, 67 (2005), 1157.  doi: 10.1016/j.bulm.2004.11.008.  Google Scholar

[15]

G. Cruz-Pacheco, L. Esteva and C. Vargas, Multi-species interactions in west nile virus infection,, Journal of Biological Dynamics, 6 (2012), 281.  doi: 10.1080/17513758.2011.571721.  Google Scholar

[16]

G. Cruz-Pacheco, L. Esteva and C. Vargas, Seasonality and outbreaks in west nile virus infection,, Bulletin of mathematical biology, 71 (2009), 1378.  doi: 10.1007/s11538-009-9406-x.  Google Scholar

[17]

B. Durand, G. Balança, T. Baldet and V. Chevalier, A metapopulation model to simulate west nile virus circulation in western africa, southern europe and the mediterranean basin,, Veterinary research, 41 ().   Google Scholar

[18]

D. S. Farner, Age groups and longevity in the american robin: Comments, further discussion, and certain revisions,, The Wilson Bulletin, (): 68.   Google Scholar

[19]

C. for Disease Control and Prevention, Statistics, surveillance, and control archive,, , (2012).   Google Scholar

[20]

C. for Disease Control and Prevention, West nile virus clinical description,, , (2012).   Google Scholar

[21]

C. for Disease Control and Prevention, West nile virus questions and answers,, , (2012).   Google Scholar

[22]

L. B. Goddard, A. E. Roth, W. K. Reisen and T. W. Scott, Vertical transmission of west nile virus by three california culex (diptera: Culicidae) species,, Journal of medical entomology, 40 (2003), 743.  doi: 10.1603/0022-2585-40.6.743.  Google Scholar

[23]

J. Heffernan, R. Smith and L. Wahl, Perspectives on the basic reproductive ratio,, Journal of the Royal Society Interface, 2 (2005), 281.  doi: 10.1098/rsif.2005.0042.  Google Scholar

[24]

A. M. Kilpatrick, A. A. Chmura, D. W. Gibbons, R. C. Fleischer, P. P. Marra and P. Daszak, Predicting the global spread of h5n1 avian influenza,, Proceedings of the National Academy of Sciences, 103 (2006), 19368.  doi: 10.1073/pnas.0609227103.  Google Scholar

[25]

A. M. Kilpatrick, L. D. Kramer, M. J. Jones, P. P. Marra and P. Daszak, West nile virus epidemics in north america are driven by shifts in mosquito feeding behavior,, PLoS Biol, 4 (2006).  doi: 10.1371/journal.pbio.0040082.  Google Scholar

[26]

N. Komar, West nile virus: epidemiology and ecology in north america,, Advances in virus research, 61 (2003), 185.   Google Scholar

[27]

J. L. Kwan, S. Kluh and W. K. Reisen, Antecedent avian immunity limits tangential transmission of west nile virus to humans,, PLoS ONE, 7 (2012).  doi: 10.1371/journal.pone.0034127.  Google Scholar

[28]

J. Mackenzie, D. Gubler and L. Petersen, Emerging flaviviruses: The spread and resurgence of japanese encephalitis, west nile and dengue viruses,, Nature medicine, 10 (2004).  doi: 10.1038/nm1144.  Google Scholar

[29]

C. A. Manore, J. K. Davis, R. C. Christofferson, D. M. Wesson, J. M. Hyman and C. N. Mores, Towards an early warning system for forecasting human west nile virus incidence,, PLoS currents, 6 (2014).  doi: 10.1371/currents.outbreaks.f0b3978230599a56830ce30cb9ce0500.  Google Scholar

[30]

C. A. Manore, K. S. Hickmann, S. Xu, H. J. Wearing and J. M. Hyman, Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus,, Journal of theoretical biology, 356 (2014), 174.  doi: 10.1016/j.jtbi.2014.04.033.  Google Scholar

[31]

R. G. McLean, S. R. Ubico, D. E. Docherty, W. R. Hansen, L. Sileo and T. S. McNamara, West nile virus transmission and ecology in birds,, Annals of the New York Academy of Sciences, 951 (2001), 54.  doi: 10.1111/j.1749-6632.2001.tb02684.x.  Google Scholar

[32]

S. Moore, C. Manore, V. Bokil, E. Borer and P. Hosseini, Spatiotemporal model of barley and cereal yellow dwarf virus transmission dynamics with seasonality and plant competition,, Bulletin of Mathematical Biology, 73 (2011), 2707.  doi: 10.1007/s11538-011-9654-4.  Google Scholar

[33]

F. Morneau, C. Lépine, R. Décarie, M.-A. Villard and J.-L. DesGranges, Reproduction of american robin (turdus migratorius) in a suburban environment,, Landscape and urban planning, 32 (1995), 55.   Google Scholar

[34]

A. T. Peterson, D. A. Vieglais and J. K. Andreasen, Migratory birds modeled as critical transport agents for west nile virus in north america,, Vector-Borne and Zoonotic Diseases, 3 (2003), 27.  doi: 10.1089/153036603765627433.  Google Scholar

[35]

Z. Qiu, Dynamics of an epidemic model with host migration,, Applied Mathematics and Computation, 218 (2011), 4614.  doi: 10.1016/j.amc.2011.10.045.  Google Scholar

[36]

W. K. Reisen, Y. Fang, H. D. Lothrop, V. M. Martinez, J. Wilson, P. O'Connor, R. Carney, B. Cahoon-Young, M. Shafii and A. C. Brault, Overwintering of west nile virus in southern california,, Journal of medical entomology, 43 (2006), 344.  doi: 10.1093/jmedent/43.2.344.  Google Scholar

[37]

W. K. Reisen, M. M. Milby and R. P. Meyer, Population dynamics of adult culex mosquitoes (diptera: Culicidae) along the kern river, kern county, california, in 1990,, Journal of medical entomology, 29 (1992), 531.  doi: 10.1093/jmedent/29.3.531.  Google Scholar

[38]

R. Rosà, G. Marini, L. Bolzoni, M. Neteler, M. Metz, L. Delucchi, E. A. Chadwick, L. Balbo, A. Mosca, M. Giacobini et al., Early warning of west nile virus mosquito vector: Climate and land use models successfully explain phenology and abundance of culex pipiens mosquitoes in north-western italy,, Parasites & vectors, 7 (2014).   Google Scholar

[39]

M. R. Sardelis, M. J. Turell, D. J. Dohm and M. L. O'Guinn, Vector competence of selected north american culex and coquillettidia mosquitoes for west nile virus,, Emerging infectious diseases, 7 (2001).   Google Scholar

[40]

J. E. Simpson, P. J. Hurtado, J. Medlock, G. Molaei, T. G. Andreadis, A. P. Galvani and M. A. Diuk-Wasser, Vector host-feeding preferences drive transmission of multi-host pathogens: West nile virus as a model system,, Proceedings of the Royal Society B: Biological Sciences, 279 (2012), 925.  doi: 10.1098/rspb.2011.1282.  Google Scholar

[41]

J. P. Swaddle and S. E. Calos, Increased avian diversity is associated with lower incidence of human west nile infection: Observation of the dilution effect,, PloS one, 3 (2008).  doi: 10.1371/journal.pone.0002488.  Google Scholar

[42]

D. Thomas and B. Urena, A model describing the evolution of west nile-like encephalitis in new york city,, Mathematical and computer modelling, 34 (2001), 771.  doi: 10.1016/S0895-7177(01)00098-X.  Google Scholar

[43]

S. Tiawsirisup, K. B. Platt, R. B. Evans and W. A. Rowley, Susceptibility of ochlerotatus trivittatus (coq.), aedes albopictus (skuse), and culex pipiens (l.) to west nile virus infection,, Vector-Borne & Zoonotic Diseases, 4 (2004), 190.   Google Scholar

[44]

S. Tiawsirisup, K. B. Platt, R. B. Evans and W. A. Rowley, A comparision of west nile virus transmission by ochlerotatus trivittatus (coq.), culex pipiens (l.), and aedes albopictus (skuse),, Vector-Borne & Zoonotic Diseases, 5 (2005), 40.   Google Scholar

[45]

M. J. Turell, M. R. Sardelis, D. J. Dohm and M. L. O'Guinn, Potential for north american mosquitoes to transmit west nile virus,, American Journal of Tropical Medicine and Hygiene, 62 (2000), 413.   Google Scholar

[46]

R. Unnasch, T. Sprenger, C. Katholi, E. Cupp, G. Hill and T. Unnasch, A dynamic transmission model of eastern equine encephalitis virus,, Ecological modelling, 192 (2006), 425.  doi: 10.1016/j.ecolmodel.2005.07.011.  Google Scholar

[47]

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

[48]

E. B. Vinogradova, Culex pipiens pipiens mosquitoes: taxonomy, distribution, ecology, physiology, genetics, applied importance and control,, Pensoft Publishers, (2000).   Google Scholar

[49]

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