### 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 language | English (US) |
---|---|

Pages (from-to) | 991-1011 |

Number of pages | 21 |

Journal | Royal Society of Edinburgh - Proceedings A |

Volume | 134 |

Issue number | 5 |

State | Published - 2004 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Royal Society of Edinburgh - Proceedings A*,

*134*(5), 991-1011.

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

Research output: Contribution to journal › Article

*Royal Society of Edinburgh - Proceedings A*, vol. 134, no. 5, pp. 991-1011.

}

TY - JOUR

T1 - Stability of steady states and existence of travelling waves in a vector-disease model

AU - Ruan, Shigui

AU - Xiao, Dongmei

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=10044257560&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044257560&partnerID=8YFLogxK

M3 - Article

VL - 134

SP - 991

EP - 1011

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 5

ER -