Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate
This paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solut...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/369072 |
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| _version_ | 1832562848434225152 |
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| author | Kai Zhou Qi-Ru Wang |
| author_facet | Kai Zhou Qi-Ru Wang |
| author_sort | Kai Zhou |
| collection | DOAJ |
| description | This paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion
model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By careful analyzsis, we derive the existence of traveling waves connecting the disease-free steady state and the endemic steady state through the establishment of the suitable upper-lower solutions. |
| format | Article |
| id | doaj-art-f27150c947ee4b0bb098927b027e6733 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f27150c947ee4b0bb098927b027e67332025-02-03T01:21:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/369072369072Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence RateKai Zhou0Qi-Ru Wang1Department of Mathematics, Chizhou University, Chizhou, Anhui 247000, ChinaSchool of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, ChinaThis paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By careful analyzsis, we derive the existence of traveling waves connecting the disease-free steady state and the endemic steady state through the establishment of the suitable upper-lower solutions.http://dx.doi.org/10.1155/2014/369072 |
| spellingShingle | Kai Zhou Qi-Ru Wang Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate Abstract and Applied Analysis |
| title | Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate |
| title_full | Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate |
| title_fullStr | Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate |
| title_full_unstemmed | Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate |
| title_short | Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate |
| title_sort | existence of traveling waves for a delayed sirs epidemic diffusion model with saturation incidence rate |
| url | http://dx.doi.org/10.1155/2014/369072 |
| work_keys_str_mv | AT kaizhou existenceoftravelingwavesforadelayedsirsepidemicdiffusionmodelwithsaturationincidencerate AT qiruwang existenceoftravelingwavesforadelayedsirsepidemicdiffusionmodelwithsaturationincidencerate |