The effect of time delay in plant--pathogen interactions with host demography
Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-12-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.473 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590144986677248 |
|---|---|
| author | Bruno Buonomo Marianna Cerasuolo |
| author_facet | Bruno Buonomo Marianna Cerasuolo |
| author_sort | Bruno Buonomo |
| collection | DOAJ |
| description | Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation. |
| format | Article |
| id | doaj-art-bee5ec3ae3294092a6c08dc15872f5c1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bee5ec3ae3294092a6c08dc15872f5c12025-01-24T02:31:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-12-0112347349010.3934/mbe.2015.12.473The effect of time delay in plant--pathogen interactions with host demographyBruno Buonomo0Marianna Cerasuolo1Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 NaplesDepartment of Mathematics, University of Portsmouth, Portsmouth, PO1 3HFBotanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.473hopf bifurcation.global stabilityepidemic modeltime delaypermanence |
| spellingShingle | Bruno Buonomo Marianna Cerasuolo The effect of time delay in plant--pathogen interactions with host demography Mathematical Biosciences and Engineering hopf bifurcation. global stability epidemic model time delay permanence |
| title | The effect of time delay in plant--pathogen interactions with host demography |
| title_full | The effect of time delay in plant--pathogen interactions with host demography |
| title_fullStr | The effect of time delay in plant--pathogen interactions with host demography |
| title_full_unstemmed | The effect of time delay in plant--pathogen interactions with host demography |
| title_short | The effect of time delay in plant--pathogen interactions with host demography |
| title_sort | effect of time delay in plant pathogen interactions with host demography |
| topic | hopf bifurcation. global stability epidemic model time delay permanence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.473 |
| work_keys_str_mv | AT brunobuonomo theeffectoftimedelayinplantpathogeninteractionswithhostdemography AT mariannacerasuolo theeffectoftimedelayinplantpathogeninteractionswithhostdemography AT brunobuonomo effectoftimedelayinplantpathogeninteractionswithhostdemography AT mariannacerasuolo effectoftimedelayinplantpathogeninteractionswithhostdemography |