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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 134, Issue 5
  • October 2004, pp. 991-1011

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

  • Shigui Ruan (a1) and Dongmei Xiao (a2)
  • DOI: http://dx.doi.org/10.1017/S0308210500003590
  • Published online: 12 July 2007
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.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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