A mathematical model for indirectly transmitted diseases

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

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

We consider a mathematical model for the indirect transmission via a contaminated environment of a microparasite between two spatially distributed host populations having non-coincident spatial domains. The parasite is benign in a first population and lethal in the second one. Global existence results are given for the resulting reaction–diffusion system coupled with an ordinary differential equation. Then, invasion and persistence of the parasite are studied. A simplified model for the transmission of a hantavirus from bank vole to human populations is then analysed.

Mots clés: Indirectly transmitted disease; Reaction–diffusion systems; Global existence; Invasion and persistence; Hantavirus

Domaines: Equations aux dérivées partielles [math.AP]

W.E. Fitzgibbon, Michel Langlais, J.J. Morgan. A mathematical model for indirectly transmitted diseases. Mathematical Biosciences, 2007, 206, pp.233-248. ⟨10.1016/j.mbs.2005.07.005⟩. ⟨hal-00195426⟩