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Modeling and control of local outbreaks of West Nile virus in the United States
1.  Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States, United States, United States 
2.  School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079 
3.  Department of Public Health Sciences, University of Miami Miller School of Medicine, Miami, FL 33136, United States 
4.  Department of Mathematics, University of Miami, Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States 
5.  Department of Geography and Regional Studies, University of Miami, Coral Gables, FL 33146, United States 
6.  Florida Department of Health, MiamiDade County, Epidemiology, Disease Control and Immunizations Services, 8600 NW 17th Street, Suite 200, Miami, FL 33126, United States 
References:
[1] 
J. F. Anderson, T. G. Andreadis, C. R. Vossbrinck, S. Tirrell, E. Wakem, A. Garmendia and H. J. Van Kruiningen, Isolation of West Nile virus from mosquitoes, crows, and a cooper's hawk in Connecticut,, Science, 286 (1999), 2331. doi: 10.1126/science.286.5448.2331. 
[2] 
W. Bajwa, M. O'Connor, B. E. Slavinski and Z. Shah, Comprehensive Mosquito Surveillance and Control Plan 2012, New York City Department of Health and Mental Hygiene, New York,, 2012. Available from: , (). 
[3] 
C. G. Blackmore, L. M. Stark, W. C. Jeter, R. L. Oliveri, R. G. Brooks, L. A. Conti and S. T. Wiersma, Surveillance results from the first West Nile virus transmission season in Florida, 2001,, The American Journal of Tropical Medicine and Hygiene, 69 (2003), 141. 
[4] 
C. Bowman, A. B. 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. 
[5] 
T. Briese, X. Y. Jia, C. Huang, L. J. Grady and W. I. Lipkin, Identification of a Kunjin/West Nile like flavivirus in brains of patients with New York encephalitis,, Lancet, 354 (1999), 1261. doi: 10.1016/S01406736(99)045766. 
[6] 
Centers for Disease Control and Prevention (CDC), West Nile Virus in the United States: Guidelines for Surveillance, Prevention, and Control,, June 4, (2013). 
[7] 
Centers for Disease Control and Prevention (CDC), West Nile Virus,, March 26, (2014). 
[8] 
J. Chen, L. Zou, Z. Jin and S. Ruan, Modeling the geographic spread of rabies in China,, PLoS Neglected Tropical Diseases, 9 (2015). doi: 10.1371/journal.pntd.0003772. 
[9] 
T. M. Colpitts, M. J. Conway, R. R. Montgomery and E. Fikrig, West Nile Virus: Biology, transmission, and human infection,, Clinical Microbiology Reviews, 25 (2012), 635. doi: 10.1128/CMR.0004512. 
[10] 
R. B. Clapp, M. K. Klimkiewicz and A. G. Futcher, Longevity records of North American birds: Columbidae through paridae,, Journal of Field Ornithology, 54 (1983), 123. 
[11] 
C. CastilloChavez and B. Song, Dynamical models of Tuberculosis and their applications,, Mathematical Biosciences and Engineering , 1 (2004), 361. doi: 10.3934/mbe.2004.1.361. 
[12] 
G. CruzPacheco, L. Esteva, J. A. MontañoHirose 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. 
[13] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations,, Journal of Mathematical Biology, 28 (1990), 365. doi: 10.1007/BF00178324. 
[14] 
O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of nextgeneration matrices for compartmental epidemic models,, Journal of the Royal Society Interface, 7 (2009). 
[15] 
M. Eidson, L. Kramer, W. Stone, Y. Hagiwara, K. Schmit and New York State West Nile Virus Avian Surveillance Team, Dead bird surveillance as an early warning system for West Nile virus,, Emerging Infectious Diseases, 7 (2001), 631. doi: 10.3201/eid0704.017405. 
[16] 
G. L. Hamer, U. D. Kitron, T. L. Goldberg, J. D. Brawn, S. R. Loss, M. O. Ruiz, D. B. Hayes and E. D. Walker, Host selection by Culex pipiens mosquitoes and West Nile virus amplification,, The American Journal of Tropical Medicine and Hygiene, 80 (2009), 268. 
[17] 
C. G. Hayes, West Nile Virus,, in The Arboviruses: Epidemiology and Ecolog (eds. T.P. Monath), (1989), 59. 
[18] 
E. B. Hayes and D. J. Gubler, West Nile Virus: Epidemiology and clinical features of an emerging epidemic in the United States,, Annual Review of Medicine, 57 (2006), 181. doi: 10.1146/annurev.med.57.121304.131418. 
[19] 
A. M. Kilpatrick, P. Daszak, M. J. Jones, P. P. Marra and L. D. Kramer, Host heterogeneity dominates West Nile virus transmission,, Proceedings of the Royal Society of London B: Biological Sciences, 273 (2006), 2327. doi: 10.1098/rspb.2006.3575. 
[20] 
N. Komar, West Nile virus: Epidemiology and ecology in North America,, Advances in Virus Research, 61 (2003), 185. 
[21] 
R. S. Lacciotti, J. T. Roehrig, V. Deubel, J. Smith and M. Parker et al., Origin of the West Nile virus responsible for an outbreak of encephalitis in the northeastern United States,, Science, 286 (1999), 2333. 
[22] 
V. Laperriere, K. Brugger and F. Rubel, Simulation of the seasonal cycles of bird, equine and human West Nile virus cases,, Preventive Veterinary Medicine, 98 (2011), 99. doi: 10.1016/j.prevetmed.2010.10.013. 
[23] 
M. A. 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/s115380059018z. 
[24] 
R. Liu, J. Shuai, J. Wu and H. Zhu, Modeling spatial spread of West Nile virus and impact of directional dispersal of birds,, Mathematical Biosciences and Engineering, 3 (2006), 145. 
[25] 
K. Magori, W. I. Bajwa, S. Bowden and J. M. Drake, Decelerating spread of West Nile Virus by percolation in a heterogeneous urban landscape,, PLoS Computational Biology, 7 (2011). doi: 10.1371/journal.pcbi.1002104. 
[26] 
N. A. Maidana and H. M. Yang, Spatial spreading of West Nile Virus described by traveling wave,, Journal of Theoretical Biology, 258 (2009), 403. doi: 10.1016/j.jtbi.2008.12.032. 
[27] 
A. A. Marfin and D. J. Gubler, West Nile encephalitis: An emerging disease in the United States,, Clinical Infectious Diseases, 33 (2001), 1712. doi: 10.1086/322700. 
[28] 
K. O. Murray, E. Mertens and P. Després, West Nile virus and its emergence in the United States of America,, Veterinary Research, 41 (2010). doi: 10.1051/vetres/2010039. 
[29] 
M. S. Nolan, J. Schuermann and K. O. Murray, West Nile virus infection among humans, Texas, USA, 20022011,, Emerging Infectious Diseases, 19 (2013), 137. doi: 10.3201/eid1901.121135. 
[30] 
D. R. O'Leary, A. A. Marfin, S. P. Montgomery, A. M. Kipp, J. A. Lehman, B. J. Biggerstaff, V. L. Elko, P. D. Collins, J. E. Jones and G. L. Campbell, The epidemic of West Nile virus in the United States,, VectorBorne and Zoonotic Diseases, 4 (2004), 61. 
[31] 
O. G. Pybus, M. A. Suchard, P. Lemey, F. J. Bernardin, A. Rambaut, F. W. Crawford, R. R. Gray, N. Arinaminpathy, S. L. Stramer, M. P. Busch and E. L. Delwart, Unifying the spatial epidemiology and molecular evolution of emerging epidemics,, Proceedings of the National Academy of Sciences, 109 (2012), 15066. doi: 10.1073/pnas.1206598109. 
[32] 
W. Reisen, H. Lothrop, R. Chiles, M. Madon, C. Cossen, L. Woods, S. Husted, V. Kramer and J. Edman, West nile virus in california,, Emerging Infectious Diseases, 10 (2004), 1369. doi: 10.3201/eid1008.040077. 
[33] 
F. Rubel, K. Brugger, M. Hantel, S. ChvalaMannsberger, T. Bakonyi, H. Weissenbock and N. Nowotny, Explaining Usutu virus dynamics in Austria: Model development and calibration,, Preventive Veterinary Medicine, 85 (2008), 166. doi: 10.1016/j.prevetmed.2008.01.006. 
[34] 
J. E. Simpson, P. J. Hurtado, J. Medlock, G. Molaei, T. G. Andreadis, A. P. Galvani and M. A. DiukWasser, Vector hostfeeding preferences drive transmission of multihost pathogens: West Nile virus as a model system,, Proceedings of the Royal Society of London B: Biological Sciences, 279 (2008), 925. doi: 10.1098/rspb.2011.1282. 
[35] 
K. E. Steele, M. J. Linn, R. J. Schoepp, N. Komar, T. W. Geisbert, R. M. Manduca, P. R. Calle, B. L. Raphael, T. L. Clippinger, T. Larsen, J. Smith, R. S. Lanciotti, N. A. Panella and T. S. Mc Namara, Pathology of fatal West Nile virus infections in native and exotic birds during the 1999 outbreak in New York City, NY,, Veterinary Pathology, 37 (2000), 208. 
[36] 
D. M. Thomas and B. Urena, A model describing the evolution of West Nilelike encephalitis in New York City,, Mathematical and Computer Modelling, 34 (2001), 771. doi: 10.1016/S08957177(01)00098X. 
[37] 
, United States Census Bureau, 2013 Historical Population Data,, last updated Sept. 25, (2013). 
[38] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29. doi: 10.1016/S00255564(02)001086. 
[39] 
H. Wan and H. Zhu, The backward bifurcation in compartmental models for West Nile virus,, Mathematical Biosciences, 227 (2010), 20. doi: 10.1016/j.mbs.2010.05.006. 
[40] 
M. J. Wonham, T. de CaminoBeck and M. A. Lewis, An epidemiological model for West Nile virus: Invasion analysis and control applications,, Proceedings of the Royal Society of London B: Biological Sciences, 271 (2004), 501. doi: 10.1098/rspb.2003.2608. 
[41] 
M. J. Wonham, M. A. Lewis, J. Renclawowicz and P. van den Driessche, Transmission assumptions generate conflicting predictions in hostvector disease models: A case study in West Nile virus,, Ecology Letters, 9 (2006), 706. doi: 10.1111/j.14610248.2006.00912.x. 
[42] 
, World Health Organization: West Nile virus,, 2015. Available from: , (). 
[43] 
J. Zhang, Z. Jin, G. Q. Sun, X. D. Sun and S. Ruan, Modeling seasonal rabies epidemic in China,, Bulletin of Mathematical Biology, 74 (2012), 1226. doi: 10.1007/s1153801297206. 
show all references
References:
[1] 
J. F. Anderson, T. G. Andreadis, C. R. Vossbrinck, S. Tirrell, E. Wakem, A. Garmendia and H. J. Van Kruiningen, Isolation of West Nile virus from mosquitoes, crows, and a cooper's hawk in Connecticut,, Science, 286 (1999), 2331. doi: 10.1126/science.286.5448.2331. 
[2] 
W. Bajwa, M. O'Connor, B. E. Slavinski and Z. Shah, Comprehensive Mosquito Surveillance and Control Plan 2012, New York City Department of Health and Mental Hygiene, New York,, 2012. Available from: , (). 
[3] 
C. G. Blackmore, L. M. Stark, W. C. Jeter, R. L. Oliveri, R. G. Brooks, L. A. Conti and S. T. Wiersma, Surveillance results from the first West Nile virus transmission season in Florida, 2001,, The American Journal of Tropical Medicine and Hygiene, 69 (2003), 141. 
[4] 
C. Bowman, A. B. 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. 
[5] 
T. Briese, X. Y. Jia, C. Huang, L. J. Grady and W. I. Lipkin, Identification of a Kunjin/West Nile like flavivirus in brains of patients with New York encephalitis,, Lancet, 354 (1999), 1261. doi: 10.1016/S01406736(99)045766. 
[6] 
Centers for Disease Control and Prevention (CDC), West Nile Virus in the United States: Guidelines for Surveillance, Prevention, and Control,, June 4, (2013). 
[7] 
Centers for Disease Control and Prevention (CDC), West Nile Virus,, March 26, (2014). 
[8] 
J. Chen, L. Zou, Z. Jin and S. Ruan, Modeling the geographic spread of rabies in China,, PLoS Neglected Tropical Diseases, 9 (2015). doi: 10.1371/journal.pntd.0003772. 
[9] 
T. M. Colpitts, M. J. Conway, R. R. Montgomery and E. Fikrig, West Nile Virus: Biology, transmission, and human infection,, Clinical Microbiology Reviews, 25 (2012), 635. doi: 10.1128/CMR.0004512. 
[10] 
R. B. Clapp, M. K. Klimkiewicz and A. G. Futcher, Longevity records of North American birds: Columbidae through paridae,, Journal of Field Ornithology, 54 (1983), 123. 
[11] 
C. CastilloChavez and B. Song, Dynamical models of Tuberculosis and their applications,, Mathematical Biosciences and Engineering , 1 (2004), 361. doi: 10.3934/mbe.2004.1.361. 
[12] 
G. CruzPacheco, L. Esteva, J. A. MontañoHirose 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. 
[13] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations,, Journal of Mathematical Biology, 28 (1990), 365. doi: 10.1007/BF00178324. 
[14] 
O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of nextgeneration matrices for compartmental epidemic models,, Journal of the Royal Society Interface, 7 (2009). 
[15] 
M. Eidson, L. Kramer, W. Stone, Y. Hagiwara, K. Schmit and New York State West Nile Virus Avian Surveillance Team, Dead bird surveillance as an early warning system for West Nile virus,, Emerging Infectious Diseases, 7 (2001), 631. doi: 10.3201/eid0704.017405. 
[16] 
G. L. Hamer, U. D. Kitron, T. L. Goldberg, J. D. Brawn, S. R. Loss, M. O. Ruiz, D. B. Hayes and E. D. Walker, Host selection by Culex pipiens mosquitoes and West Nile virus amplification,, The American Journal of Tropical Medicine and Hygiene, 80 (2009), 268. 
[17] 
C. G. Hayes, West Nile Virus,, in The Arboviruses: Epidemiology and Ecolog (eds. T.P. Monath), (1989), 59. 
[18] 
E. B. Hayes and D. J. Gubler, West Nile Virus: Epidemiology and clinical features of an emerging epidemic in the United States,, Annual Review of Medicine, 57 (2006), 181. doi: 10.1146/annurev.med.57.121304.131418. 
[19] 
A. M. Kilpatrick, P. Daszak, M. J. Jones, P. P. Marra and L. D. Kramer, Host heterogeneity dominates West Nile virus transmission,, Proceedings of the Royal Society of London B: Biological Sciences, 273 (2006), 2327. doi: 10.1098/rspb.2006.3575. 
[20] 
N. Komar, West Nile virus: Epidemiology and ecology in North America,, Advances in Virus Research, 61 (2003), 185. 
[21] 
R. S. Lacciotti, J. T. Roehrig, V. Deubel, J. Smith and M. Parker et al., Origin of the West Nile virus responsible for an outbreak of encephalitis in the northeastern United States,, Science, 286 (1999), 2333. 
[22] 
V. Laperriere, K. Brugger and F. Rubel, Simulation of the seasonal cycles of bird, equine and human West Nile virus cases,, Preventive Veterinary Medicine, 98 (2011), 99. doi: 10.1016/j.prevetmed.2010.10.013. 
[23] 
M. A. 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/s115380059018z. 
[24] 
R. Liu, J. Shuai, J. Wu and H. Zhu, Modeling spatial spread of West Nile virus and impact of directional dispersal of birds,, Mathematical Biosciences and Engineering, 3 (2006), 145. 
[25] 
K. Magori, W. I. Bajwa, S. Bowden and J. M. Drake, Decelerating spread of West Nile Virus by percolation in a heterogeneous urban landscape,, PLoS Computational Biology, 7 (2011). doi: 10.1371/journal.pcbi.1002104. 
[26] 
N. A. Maidana and H. M. Yang, Spatial spreading of West Nile Virus described by traveling wave,, Journal of Theoretical Biology, 258 (2009), 403. doi: 10.1016/j.jtbi.2008.12.032. 
[27] 
A. A. Marfin and D. J. Gubler, West Nile encephalitis: An emerging disease in the United States,, Clinical Infectious Diseases, 33 (2001), 1712. doi: 10.1086/322700. 
[28] 
K. O. Murray, E. Mertens and P. Després, West Nile virus and its emergence in the United States of America,, Veterinary Research, 41 (2010). doi: 10.1051/vetres/2010039. 
[29] 
M. S. Nolan, J. Schuermann and K. O. Murray, West Nile virus infection among humans, Texas, USA, 20022011,, Emerging Infectious Diseases, 19 (2013), 137. doi: 10.3201/eid1901.121135. 
[30] 
D. R. O'Leary, A. A. Marfin, S. P. Montgomery, A. M. Kipp, J. A. Lehman, B. J. Biggerstaff, V. L. Elko, P. D. Collins, J. E. Jones and G. L. Campbell, The epidemic of West Nile virus in the United States,, VectorBorne and Zoonotic Diseases, 4 (2004), 61. 
[31] 
O. G. Pybus, M. A. Suchard, P. Lemey, F. J. Bernardin, A. Rambaut, F. W. Crawford, R. R. Gray, N. Arinaminpathy, S. L. Stramer, M. P. Busch and E. L. Delwart, Unifying the spatial epidemiology and molecular evolution of emerging epidemics,, Proceedings of the National Academy of Sciences, 109 (2012), 15066. doi: 10.1073/pnas.1206598109. 
[32] 
W. Reisen, H. Lothrop, R. Chiles, M. Madon, C. Cossen, L. Woods, S. Husted, V. Kramer and J. Edman, West nile virus in california,, Emerging Infectious Diseases, 10 (2004), 1369. doi: 10.3201/eid1008.040077. 
[33] 
F. Rubel, K. Brugger, M. Hantel, S. ChvalaMannsberger, T. Bakonyi, H. Weissenbock and N. Nowotny, Explaining Usutu virus dynamics in Austria: Model development and calibration,, Preventive Veterinary Medicine, 85 (2008), 166. doi: 10.1016/j.prevetmed.2008.01.006. 
[34] 
J. E. Simpson, P. J. Hurtado, J. Medlock, G. Molaei, T. G. Andreadis, A. P. Galvani and M. A. DiukWasser, Vector hostfeeding preferences drive transmission of multihost pathogens: West Nile virus as a model system,, Proceedings of the Royal Society of London B: Biological Sciences, 279 (2008), 925. doi: 10.1098/rspb.2011.1282. 
[35] 
K. E. Steele, M. J. Linn, R. J. Schoepp, N. Komar, T. W. Geisbert, R. M. Manduca, P. R. Calle, B. L. Raphael, T. L. Clippinger, T. Larsen, J. Smith, R. S. Lanciotti, N. A. Panella and T. S. Mc Namara, Pathology of fatal West Nile virus infections in native and exotic birds during the 1999 outbreak in New York City, NY,, Veterinary Pathology, 37 (2000), 208. 
[36] 
D. M. Thomas and B. Urena, A model describing the evolution of West Nilelike encephalitis in New York City,, Mathematical and Computer Modelling, 34 (2001), 771. doi: 10.1016/S08957177(01)00098X. 
[37] 
, United States Census Bureau, 2013 Historical Population Data,, last updated Sept. 25, (2013). 
[38] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29. doi: 10.1016/S00255564(02)001086. 
[39] 
H. Wan and H. Zhu, The backward bifurcation in compartmental models for West Nile virus,, Mathematical Biosciences, 227 (2010), 20. doi: 10.1016/j.mbs.2010.05.006. 
[40] 
M. J. Wonham, T. de CaminoBeck and M. A. Lewis, An epidemiological model for West Nile virus: Invasion analysis and control applications,, Proceedings of the Royal Society of London B: Biological Sciences, 271 (2004), 501. doi: 10.1098/rspb.2003.2608. 
[41] 
M. J. Wonham, M. A. Lewis, J. Renclawowicz and P. van den Driessche, Transmission assumptions generate conflicting predictions in hostvector disease models: A case study in West Nile virus,, Ecology Letters, 9 (2006), 706. doi: 10.1111/j.14610248.2006.00912.x. 
[42] 
, World Health Organization: West Nile virus,, 2015. Available from: , (). 
[43] 
J. Zhang, Z. Jin, G. Q. Sun, X. D. Sun and S. Ruan, Modeling seasonal rabies epidemic in China,, Bulletin of Mathematical Biology, 74 (2012), 1226. doi: 10.1007/s1153801297206. 
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