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Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion
This paper is concerned with the existence of travlelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this sys...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2011
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3123341/ https://www.ncbi.nlm.nih.gov/pubmed/21731655 http://dx.doi.org/10.1371/journal.pone.0021128 |
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author | Yang, Jing Liang, Siyang Zhang, Yi |
author_facet | Yang, Jing Liang, Siyang Zhang, Yi |
author_sort | Yang, Jing |
collection | PubMed |
description | This paper is concerned with the existence of travlelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results. |
format | Online Article Text |
id | pubmed-3123341 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2011 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-31233412011-06-30 Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion Yang, Jing Liang, Siyang Zhang, Yi PLoS One Research Article This paper is concerned with the existence of travlelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results. Public Library of Science 2011-06-24 /pmc/articles/PMC3123341/ /pubmed/21731655 http://dx.doi.org/10.1371/journal.pone.0021128 Text en Yang et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Yang, Jing Liang, Siyang Zhang, Yi Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title | Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title_full | Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title_fullStr | Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title_full_unstemmed | Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title_short | Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion |
title_sort | travelling waves of a delayed sir epidemic model with nonlinear incidence rate and spatial diffusion |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3123341/ https://www.ncbi.nlm.nih.gov/pubmed/21731655 http://dx.doi.org/10.1371/journal.pone.0021128 |
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