Modeling the circulation of a disease between two host populations on non coincident spatial domains

W.E. Fitzgibbon , Michel Langlais (1, 2) , F. Marpeau , J.J. Morgan

1 IMB - Institut de Mathématiques de Bordeaux
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics

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.

Mots clés: distinct spatial domains; large-time behavior; reaction–diffusion equations

Domaines: Equations aux dérivées partielles [math.AP]

W.E. Fitzgibbon, Michel Langlais, F. Marpeau, J.J. Morgan. Modeling the circulation of a disease between two host populations on non coincident spatial domains. Biological Invasions, 2005, 7, pp.863-875. ⟨10.1007/s10530-005-5210-1⟩. ⟨hal-00195425⟩