BIRDS MOVEMENT IMPACT ON THE TRANSMISSION OF WEST NILE VIRUS BETWEEN PATCHES

Juping Zhang; Zhen Jin; Huaiping Zhu

doi:10.11948/2018.443

2018 Volume 8 Issue 2

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Juping Zhang, Zhen Jin, Huaiping Zhu. BIRDS MOVEMENT IMPACT ON THE TRANSMISSION OF WEST NILE VIRUS BETWEEN PATCHES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 443-456. doi: 10.11948/2018.443

Citation:

Juping Zhang, Zhen Jin, Huaiping Zhu. BIRDS MOVEMENT IMPACT ON THE TRANSMISSION OF WEST NILE VIRUS BETWEEN PATCHES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 443-456. doi: 10.11948/2018.443

BIRDS MOVEMENT IMPACT ON THE TRANSMISSION OF WEST NILE VIRUS BETWEEN PATCHES

1 Complex Systems Research Center, Shanxi University, Taiyuan City, Shanxi Province, 030006, China;
2 Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan City, Shanxi Province, 030006, China;
3 LAMPS and Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

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Abstract

Abstract

Spatial heterogeneity plays an important role in the distribution and persistence of many infectious disease. In the paper, a multi-patch model for the spread of West Nile virus among n discrete geographic regions is presented that incorporates a mobility process. In the mobility process, we assume that the birds can move among regions, but not the mosquitoes based on scalespace. We show that the movement of birds between patches is sufficient to maintain disease persistence in patches. We compute the basic reproduction number R₀. We prove that if R₀<1, then the disease-free equilibrium of the model is globally asymptotically stable. When R₀>1, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between two regions.
- West Nile virus /
- patch model /
- birds movement /
- basic reproduction number /
- stability
MSC: 34A34;34D23

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References

[1]	P. Auger, E. Kouokam, G. Sallet, M. Tchuente and B. Tsanou, The RossMacdonald model in a patchy environment, Math. Biosci., 2008, 216(2), 123-131. Google Scholar
[2]	C. H. Calisher, K. S. C. Maness, R. D. Lord and P. H. Coleman, Identification of two South American strains of eastern equine encephalomyelitis virus from migrant birds captured on the Mississippi Delta, Am. J. Epidemiol., 1971, 94(2), 172-178. Google Scholar
[3]	G. Cruz-Pacheco, L. Esteva, J. A. Montaño-Hirose and C. Vargas, Modelling the dynamics of West Nile virus, Bull. Math. Biol., 2005, 67(6), 1157-1172. Google Scholar
[4]	C. Cosner, J. C. Beier, R. S. Cantrell, D. Impoinvil, L. Kapitanski, M. D. Potts, A. Troyo and S. Ruan, The effect of human movement on the persistence of vector-borne diseases, J. Theor. Biol., 2009, 258(4), 550-560. Google Scholar
[5]	V. Capasso, Mathematical structures of epidemic systems, Springer, Berlin, 1993. Google Scholar
[6]	C. Dye and G. Hasibeder, Population dynamics of mosquito-borne disease:effects of flies which bite some people more frequently than others, Transactions of the Royal Society of Tropical Medicine and Hygiene, 1986, 80(1), 69-77. Google Scholar
[7]	D. Gao and S. Ruan, A multipatch malaria model with logistic growth populations, SIAM J. Appl. Math., 2012, 72(3), 819-841. Google Scholar
[8]	G. Hasibeder and C. Dye, Population dynamics of mosquito-borne disease:persistence in a completely heterogeneous environment, Theor. Popul. Biol., 1988, 33(1), 31-53. Google Scholar
[9]	N. Karabatsos, International catalogue of arboviruses including certain other viruses of vertebrates, American Society of Tropical Medicine and Hygiene, San Antonio, 1985. Google Scholar
[10]	M. Y. Li and Z. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Differ. Equations, 2010, 248(1), 1-20. Google Scholar
[11]	J. P. LaSalle, The Stability of Dynamical Systems(CBMS-NSF Regional Conference Series in Applied Mathematics) Paperback, Society for Industrial and Applied Mathematics, New York, 1987. Google Scholar
[12]	R. Liu, J. Shuai, J. Wu and H. Zhu, Modeling spatial spread of West Nile virus and impact of directional dispersal of birds, Math. Biosci. Eng., 2006, 3(1), 145-160. Google Scholar
[13]	R. D. Lord and C.H. Calisher, Further evidence of southward transport of arboviruses by migratory birds, Am. J. Epidemiol. 1970, 92(1), 73-78. Google Scholar
[14]	Z. Ma, Y. Zhou and J. Wu, Modeling and dynamics of infectious diseases, Higher Education Press, Beijing, 2009. Google Scholar
[15]	J. Owen, F. Moore, N. Panella, et al., Migrating birds as dispersal vehicles for West Nile virus, EcoHealth, 2006, 3(2),79-85. Google Scholar
[16]	J. H. Rappole, S. R. Derrickson and Z. Hubalek, Migratory birds and spread of West Nile virus in the Western Hemisphere, Emerg. Infect. Dis., 2000, 6(4), 319-328. Google Scholar
[17]	J. H. Rappole and Z. Hubalek, Migratory birds and West Nile virus, J. Appl. Microbiol., 2003, 94(s1), 47-58. Google Scholar
[18]	D. J. Rodriguez and L. Torres-Sorando, Models of infectious diseases in spatially heterogeneous environments, Bull. Math. Biol., 2001, 63(3), 547-571. Google Scholar
[19]	K. C. Smithburn, T. P. Hughes, A. W. Burke, and J. H. Paul, A neurotropic virus isolated from the blood of a native of Uganda. Am. J. Trop. Med. Hyg., 1940, 4, 471-492. Google Scholar
[20]	K. E. Steele, M. J. Linn, R. J. Schoepp, N. Komar, T. W. Geisbert, R. M. Manduca, et al., Pathology of fatal West Nile virus infections in native and exotic birds during the 1999 outbreak in New York City, New York, Vet Pathol., 2000, 37(3), 208-224. Google Scholar
[21]	D. L. Smith and F. E. McKenzie, Statics and dynamics of malaria infection in Anopheles mosquitoes, Malaria J., 2004, 3(1), 13-26. Google Scholar
[22]	L. Torres-Sorando and D. J. Rodriguez, Models of spatio-temporal dynamics in malaria, Ecol. Model., 1997, 104(2-3), 231-240. Google Scholar
[23]	Y. Takeuchi, K. Sato and Y. Iwasa, Mathematics for Life Science and Medicine, Springer, Berlin, 2007. Google Scholar
[24]	P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 2002, 180(1), 29-48. Google Scholar
[25]	M. J. Wonham, T. de-Camino-Beck and M. Lewis, An epidemiological model for West Nile virus:invasion analysis and control applications, Proc. R. Soc. Lond. B, 2004, 271(1538), 501-507. Google Scholar
[26]	W. D. Wang and X. Q. Zhao, An epidemic model in a patchy environment, Math. Biosci., 2004, 190(1), 97-112. Google Scholar