Advertisement

Modelling the dynamics of West Nile Virus

  • Gustavo Cruz-Pacheco
  • Lourdes Esteva
  • Juan Antonio Montaõ-Hirose
  • Cristobal VargasEmail author
Article

Abstract

In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number \(\tilde R_0 \) in terms of measurable epidemiological and demographic parameters. \(\tilde R_0 \) is the threshold condition that determines the dynamics of WNV infection: if \(\tilde R_0 \leqslant 1\) the disease fades out, and for \(\tilde R_0 > 1\) the disease remains endemic. Using experimental and field data we estimate \(\tilde R_0 \) for several species of birds. Numerical simulations of the temporal course of the infected bird proportion show damped oscillations approaching the endemic value.

Keywords

West Nile Virus Vertical Transmission Endemic Equilibrium House Sparrow Infectious Period 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Baqar, S., Hayes, C.G., Murphy, J.R., Watts, D.M., 1993. Vertical transmission of West Nile Virus by Culex and Aedes species mosquitoes. Am. J. Trop. Med. Hyg. 48, 757–762.Google Scholar
  2. Blitvich, B.J., Fernández-Salas, I.F., Contreras-Cordero, J.F., Marlenee, N.L., Gonzalez-Rojas, J.I. et al., 2003. Serological evidence of West Nile Virus infection in horses, Coahuila State, México. Emerg. Infect. Dis. 9(7), 853–856.Google Scholar
  3. Campbell, L.G., Martin, A.A., Lanciotti, R.S., Gubler, D.J., 2002. West Nile Virus. The Lancet Infect. Dis. 2, 519–529.CrossRefGoogle Scholar
  4. Center for Disease Control and Prevention (CDC), 1999. Update: West Nile-like viral encephalitis-New York, 1999. Morb. Mortal Wkly. Rep. 48, 890–892.Google Scholar
  5. Center for Disease Control and Prevention (CDC), 2001. Weekly update: West Nile virus activity-United States, November 14–20, 2001. Morb. Mortal Wkly. Rep. 50, 1061–1063.Google Scholar
  6. Center for Disease Control and Prevention (CDC), 2004. CDC-West Nile Virus-Surveillance and Control Case Count of West Nile Disease. www.cdc.gov/ncidod/dvbid/westnile/.Google Scholar
  7. Coddington, E.A., Levinson, N., 1955. Theory of Ordinary Differential Equations. McGraw-Hill, New York.zbMATHGoogle Scholar
  8. Dohm, D.J., Sardelis, M.R., Turell, M.J., 2002. Experimental vertical transmission of West Nile Virus by Culex pipiens (Diptera: Culicidae). J. Med. Entomol. 39(4), 640–644.Google Scholar
  9. Esteva, L., Vargas, C., 1998. Analysis of a dengue disease transmission model. Math. Biosci. 150, 131–151.CrossRefzbMATHGoogle Scholar
  10. Estrada-Franco, J.G., Navarro-López, R., Beasley, D.W.C., Coffey, L., Carrara, A.S. et al., 2003. West Nile Virus in Mexico: Evidence of widespread circulation since July 2002. Emerg. Infect. Dis. 9(12), 1604–1607.Google Scholar
  11. Goddard, L.B., Roth, A.E., Reisen, W.K., Scott, T.W., 2003. Vertical transmission of West Nile Virus by three California Culex (Diptera: Culicidae) species. J. Med. Entomol. 40(6), 743–746.CrossRefGoogle Scholar
  12. Gubler, D.J., 1986. Dengue. In: Monath, T.P. (Ed.), The Arboviruses: Epidemiology and Ecology, vol. II. CRC Press, Florida, pp. 213–261.Google Scholar
  13. Hale, J.K., 1969. Ordinary Differential Equations. John Wiley and Sons, New York.zbMATHGoogle Scholar
  14. Hayes, C.G., 1989. West Nile fever. In: Monath, T.P. (Ed.), The arboviruses: Epidemiology and Ecology, vol. V. CRC Press, Florida, pp. 59–88.Google Scholar
  15. Komar, N., Langevin, S., Hinten, S., Nemeth, N., Edwards, E. et al., 2003. Experimental infection of North American birds with the New York 1999 strain of West Nile Virus. Emerg. Infect. Dis. 9(3), 311–322.Google Scholar
  16. Lanciotti, R.S., Rohering, J.T., Deubel, V., Smith, J., Parker, M. et al., 1999. Origin of the West Nile Virus responsible for an outbreak of Encephalitis in the Northeastern United States. Science 286, 2333–2337.CrossRefGoogle Scholar
  17. Loroño-Pinto, M.A., Blitvich, B.J., Farfán-Ale, J.A., Puerto, F.I., Blanco, J.M. et al., 2003. Serologic evidence of West Nile Virus infection in horses, Yucatan State, México. Emerg. Infect. Dis. 9(7), 857–859.Google Scholar
  18. Montaño-Hirose, J.A., 2002. El virus de la fiebre del Oeste del Nilo. Imagen Veterinaria 2(8), 7–10.Google Scholar
  19. Oliver Jr., L.A., 1961a. Crows and Jays-Corvidae. In: Birds of the World. Golden Press, New York.Google Scholar
  20. Oliver Jr., L.A., 1961b. Gulls and Terns-Laridae. In: Birds of the World. Golden Press, New York.Google Scholar
  21. SSa, 2004. Centro Nacional de Vigilancia Epidemiológica de la Secretaría de Salud de México. http://www.cenave.gob.mx/von/.
  22. Swayne, D.E., Beck, J.R., Zaki, S., 2000. Pathogenicity of West Nile virus for turkeys. Avian Diseases 44, 932–937.CrossRefGoogle Scholar
  23. Tesh, R.B., Travassos da Rosa, A.P.A., Guzmán, H., Araujo, T.P., Xiao, S.Y., 2002. Immunization with heterologous flaviviruses protective against fatal West Nile Encephalitis. Emerg. Infect. Dis. 8(3), 246–251.CrossRefGoogle Scholar
  24. The University of Michigan Museum of Zoology, 2004. Animal Diversity Web. http://www.animaldiversity.ummz.umich.edu.
  25. Vargas-García, R., Cárdenas Lara, J., 2002. Mosquitos ornitofílicos transmisores de la encefalitis del Oeste del Nilo en el mundo. Imagen Veterinaria 2(8), 11–15.Google Scholar

Copyright information

© Society for Mathematical Biology 2005

Authors and Affiliations

  • Gustavo Cruz-Pacheco
    • 1
  • Lourdes Esteva
    • 2
  • Juan Antonio Montaõ-Hirose
    • 3
  • Cristobal Vargas
    • 4
    Email author
  1. 1.IIMASUNAMMéxico, D.F.Mexico
  2. 2.Departamento de Matemáticas, Facultad de CienciasUNAMMéxico, D.F.Mexico
  3. 3.Instituto de Ciencias AgropecuariasUAEHTulancingo, Hgo.Mexico
  4. 4.Departamento de Control AutomáticoCINVESTAV-IPNMéxico, D.F.Mexico

Personalised recommendations