Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modeling spatial spread of west nile virus and impact of directional dispersal of birds

1. Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3
2. Public Health Agency of Canada, Division of Enteric, Foodborne and Waterborne Diseases, 160 Research Lane, Guelph, ON, N1G 5B2

A patchy model for the spatial spread of West Nile virus is formulated and analyzed. The basic reproduction number is calculated and compared for different long-range dispersal patterns of birds, and simulations are carried out to demonstrate discontinuous or jump spatial spread of the virus when the birds' long-range dispersal dominates the nearest neighborhood interaction and diffusion of mosquitoes and birds.
  Article Metrics

Keywords transmission; spatial control.; West Nile virus (WNv); mosquitoes and birds; reproduction number; differential equations; patch model

Citation: Rongsong Liu, Jiangping Shuai, Jianhong Wu, Huaiping Zhu. Modeling spatial spread of west nile virus and impact of directional dispersal of birds. Mathematical Biosciences and Engineering, 2006, 3(1): 145-160. doi: 10.3934/mbe.2006.3.145


This article has been cited by

  • 1. , , Stochastic Calculus for Fractional Brownian Motion and Related Processes, 2008, Chapter 4, 291, 10.1007/978-3-540-75873-0_4
  • 2. S. A. Gourley, R. Liu, J. Wu, , Structured Population Models in Biology and Epidemiology, 2008, Chapter 4, 165, 10.1007/978-3-540-78273-5_4
  • 3. Ruixia Zhang, Global dynamic analysis of a model for vector-borne diseases on bipartite networks, Physica A: Statistical Mechanics and its Applications, 2019, 123813, 10.1016/j.physa.2019.123813
  • 4. Fuxiang Li, Junli Liu, Xiao-Qiang Zhao, A West Nile Virus Model with Vertical Transmission and Periodic Time Delays, Journal of Nonlinear Science, 2020, 30, 1, 449, 10.1007/s00332-019-09579-8
  • 5. Junli Liu, Tailei Zhang, Qiaoling Chen, A Periodic West Nile Virus Transmission Model with Stage-Structured Host Population, Complexity, 2020, 2020, 1, 10.1155/2020/2050587
  • 6. M. J. Wonham, M. A. Lewis, , Mathematical Epidemiology, 2008, Chapter 14, 365, 10.1007/978-3-540-78911-6_14
  • 7. Abdelrazig K. Tarboush, Zhengdi Zhang, The Diffusive Model for West Nile Virus on a Periodically Evolving Domain, Complexity, 2020, 2020, 1, 10.1155/2020/6280313
  • 8. Kaifa Wang, Wendi Wang, Shiping Song, Dynamics of an HBV model with diffusion and delay, Journal of Theoretical Biology, 2008, 253, 1, 36, 10.1016/j.jtbi.2007.11.007
  • 9. Jianhong Wu, , Mathematical Epidemiology, 2008, Chapter 8, 191, 10.1007/978-3-540-78911-6_8
  • 10. Tomás de-Camino-Beck, Mark A. Lewis, P. van den Driessche, A graph-theoretic method for the basic reproduction number in continuous time epidemiological models, Journal of Mathematical Biology, 2009, 59, 4, 503, 10.1007/s00285-008-0240-9
  • 11. Jifa Jiang, Zhipeng Qiu, Jianhong Wu, Huaiping Zhu, Threshold Conditions for West Nile Virus Outbreaks, Bulletin of Mathematical Biology, 2009, 71, 3, 627, 10.1007/s11538-008-9374-6
  • 12. C. Cosner, J.C. Beier, R.S. Cantrell, D. Impoinvil, L. Kapitanski, M.D. Potts, A. Troyo, S. Ruan, The effects of human movement on the persistence of vector-borne diseases, Journal of Theoretical Biology, 2009, 258, 4, 550, 10.1016/j.jtbi.2009.02.016
  • 13. Jifa Jiang, Zhipeng Qiu, The Complete Classification for Dynamics in a Nine-Dimensional West Nile Virus Model, SIAM Journal on Applied Mathematics, 2009, 69, 5, 1205, 10.1137/070709438
  • 14. Hui Wan, Huaiping Zhu, The backward bifurcation in compartmental models for West Nile virus, Mathematical Biosciences, 2010, 227, 1, 20, 10.1016/j.mbs.2010.05.006
  • 15. Vincent Laperriere, Katharina Brugger, Franz Rubel, Simulation of the seasonal cycles of bird, equine and human West Nile virus cases, Preventive Veterinary Medicine, 2011, 98, 2-3, 99, 10.1016/j.prevetmed.2010.10.013
  • 16. Gustavo Cruz-Pacheco, Lourdes Esteva, Cristobal Vargas, Multi-species interactions in West Nile virus infection, Journal of Biological Dynamics, 2012, 6, 2, 281, 10.1080/17513758.2011.571721
  • 17. Zhengdi Zhang, Abdelrazig K. Tarboush, The diffusive model for West Nile virus with advection and expanding fronts in a heterogeneous environment, International Journal of Biomathematics, 2020, 10.1142/S1793524520500576

Reader Comments

your name: *   your email: *  

Copyright Info: 2006, Rongsong Liu, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved