Multiple travelling waves for an SI-epidemic model
Language
en
Article de revue
This item was published in
Networks and Heterogeneous Media. 2013, vol. 8, n° 1, p. 171-190
American Institute of Mathematical Sciences
English Abstract
In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. The dynamics of the underlying system of ordinary differential ...Read more >
In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. The dynamics of the underlying system of ordinary differential equations are first shown to exhibit an infinite number of heteroclinic orbits connecting the trivial equilibrium with an interior equilibrium. Our mathematical study of the corresponding reaction-diffusion system is concerned with travelling wave solutions. Based on a detailed study of the center-unstable manifold around the interior equilibrium, we are able to prove the existence of an infinite number of travelling wave solutions connecting the trivial equilibrium and the interior equilibrium.Read less <
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