Itinéraires de contagions

Siegfried, André; Vallery-Radot, P

doi:10.1522/030294755

Cited by 3 publications

(2 citation statements)

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“…The purpose of this model is to understand the effect of a line interacting with a homogeneous environment. This type of questions arises for instance in studying the propagation of diseases directed by roads [10] or the movements of animal populations in the presence of pathways allowing for a more rapid movement. An example of the latter is provided by recent observations of movements of wolves along seismic lines in Western Canada [9].…”

Section: Introductionmentioning

confidence: 99%

Fisher–KPP propagation in the presence of a line: further effects

Berestycki¹,

Roquejoffre

Rossi

2013

Nonlinearity

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This paper is a continuation of [4] where a new model of biological invasions in the plane directed by a line was introduced. Here we include new features such as transport and reaction terms on the line. Their interaction with the pure diffusivity in the plane is quantified in terms of enhancement of the propagation speed. We establish conditions that determine whether the spreading speed exceeds the standard Fisher KPP invasion speed. These conditions involve the ratio of the diffusivities on the line and in the field, the transport term and the reactions. We derive the asymptotic behaviour for large diffusions or large transports. We also discuss the biological interpretation of these findings.

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Section: Introductionmentioning

confidence: 99%

Fisher–KPP propagation in the presence of a line: further effects

Berestycki¹,

Roquejoffre

Rossi

2013

Nonlinearity

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show abstract

“…It then also spread more slowly away from the roads, inland, bringing about a dramatic invasion. See, for instance, the account by [36]. More recently, it has been observed that invasive species such as the Processionary caterpillar of the pine tree in Europe, have been moving faster than anticipated.…”

Section: Motivationmentioning

confidence: 99%