Two-patch model for the spread of West Nile virus

Juping Zhang, George Cosner, Huaiping Zhu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 (Formula presented.) is computed by the next generation matrix method. We prove that if (Formula presented.), then the disease-free equilibrium is globally asymptotically stable. If (Formula presented.), 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 (Formula presented.) in terms of the birds movement rate are performed which show that the impacts could be very complicated.

Original languageEnglish (US)
Pages (from-to)1-24
Number of pages24
JournalBulletin of Mathematical Biology
DOIs
StateAccepted/In press - Feb 28 2018

Fingerprint

West Nile virus
Birds
Viruses
Virus
Patch
bird
Endemic Equilibrium
birds
Globally Asymptotically Stable
Basic Reproduction Number
Endemic Diseases
Numerical Simulation
Basic Reproduction number
Computer simulation
Matrix Method
Culicidae
mosquito
Model
Perturbation Theory
simulation

Keywords

  • 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

Cite this

Two-patch model for the spread of West Nile virus. / Zhang, Juping; Cosner, George; Zhu, Huaiping.

In: Bulletin of Mathematical Biology, 28.02.2018, p. 1-24.

Research output: Contribution to journalArticle

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