Biological Invasions

, Volume 7, Issue 5, pp 863–875 | Cite as

Modeling the Circulation of a Disease Between Two Host Populations on non Coincident Spatial Domains

  • W.–-E. Fitzgibbon
  • M. Langlais
  • F. Marpeau
  • J.-–J. Morgan
Article

Abstract

We derive a reaction–diffusion system modeling the spatial propagation of a disease with kinetics occurring on distinct spatial domains. This corresponds to the actual invasion of a disease from a species living in a given spatial domain toward a second species living in a different spatial domain. We study the global existence of solutions and discuss the long time behavior of solutions. Then we consider a special case, based on a model of brain worm infection from white-tailed deer to moose populations, for which we discuss the invasion success/failure process and disprove a conjecture stated in an earlier work.

Keywords

 distinct spatial domains large-time behavior reaction–diffusion equations 

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Copyright information

© Springer 2005

Authors and Affiliations

  • W.–-E. Fitzgibbon
    • 1
  • M. Langlais
    • 2
  • F. Marpeau
    • 3
  • J.-–J. Morgan
    • 4
  1. 1.Departments of Engineering Technology and MathematicsUniversity of HoustonHoustonUSA
  2. 2.MAB, UMR CNRS 5466Bordeaux CedexFrance
  3. 3.MAB, UMR CNRS 5466Talence CedexFrance
  4. 4.Department of MathematicsUniversity of HoustonHoustonUSA

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