Stability of steady states and existence of travelling waves in a vector-disease model

Shigui Ruan, Dongmei Xiao

Research output: Contribution to journalArticle

95 Citations (Scopus)

Abstract

In this paper, a host-vector model is considered for a disease without immunity in which the current density of infectious vectors is related to the number of infectious hosts at earlier times. Spatial spread in a region is modelled in the partial integro-differential equation by a diffusion term. For the general model, we first study the stability of the steady states using the contracting-convex-sets technique. When the spatial variable is one dimensional and the delay kernel assumes some special form, we establish the existence of travelling wave solutions by using the linear chain trick and the geometric singular perturbation method.

Original languageEnglish (US)
Pages (from-to)991-1011
Number of pages21
JournalRoyal Society of Edinburgh - Proceedings A
Volume134
Issue number5
StatePublished - 2004

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Traveling Wave
Partial Integro-differential Equation
Singular Perturbation Method
Integrodifferential equations
Immunity
Traveling Wave Solutions
Convex Sets
Current density
kernel
Term
Model
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Stability of steady states and existence of travelling waves in a vector-disease model. / Ruan, Shigui; Xiao, Dongmei.

In: Royal Society of Edinburgh - Proceedings A, Vol. 134, No. 5, 2004, p. 991-1011.

Research output: Contribution to journalArticle

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