Modelling the dynamics of West Nile Virus

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


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.


West Nile Virus Vertical Transmission Endemic Equilibrium House Sparrow Infectious Period 
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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

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