Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay
In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positi...
| Main Authors: | , , |
|---|---|
| Format: | Journal Article |
| Published: |
Pergamon, Elsevier Ltd
2010
|
| Online Access: | http://hdl.handle.net/20.500.11937/39957 |
| _version_ | 1848755736083955712 |
|---|---|
| author | Peng, Yahong Zhang, Tonghua Tade, Moses |
| author_facet | Peng, Yahong Zhang, Tonghua Tade, Moses |
| author_sort | Peng, Yahong |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positions from their possible positions at previous times. We shall show that such fronts exist for the weak generic delay kernel and sufficiently small delays by using geometric singular perturbation theory. Then, for the discrete-delay case, following Canosa’s asymptotic analysis method, we give some information on travelling front solutions. |
| first_indexed | 2025-11-14T09:01:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-39957 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:01:02Z |
| publishDate | 2010 |
| publisher | Pergamon, Elsevier Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-399572017-09-13T15:09:37Z Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay Peng, Yahong Zhang, Tonghua Tade, Moses In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positions from their possible positions at previous times. We shall show that such fronts exist for the weak generic delay kernel and sufficiently small delays by using geometric singular perturbation theory. Then, for the discrete-delay case, following Canosa’s asymptotic analysis method, we give some information on travelling front solutions. 2010 Journal Article http://hdl.handle.net/20.500.11937/39957 10.1016/j.nonrwa.2009.08.004 Pergamon, Elsevier Ltd restricted |
| spellingShingle | Peng, Yahong Zhang, Tonghua Tade, Moses Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title | Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title_full | Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title_fullStr | Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title_full_unstemmed | Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title_short | Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| title_sort | existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay |
| url | http://hdl.handle.net/20.500.11937/39957 |