Two-patch model for the spread of West Nile virus

Juping Zhang, Chris Cosner, Huaiping Zhu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number R0 is computed by the next generation matrix method. We prove that if R0< 1 , then the disease-free equilibrium is globally asymptotically stable. If R0> 1 , the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for R0 in terms of the birds movement rate are performed which show that the impacts could be very complicated.

Original languageEnglish (US)
Pages (from-to)840-863
Number of pages24
JournalBulletin of Mathematical Biology
Issue number4
StatePublished - Apr 1 2018


  • Basic reproduction number
  • Birds migration
  • Mosquitoes
  • Patch model
  • Stability
  • West Nile virus

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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