Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission
In the present research, we study a mathematical model for vector-borne plant disease with the plant resistance to disease and vector crowding effect and propose using Beddington-DeAngelis type disease transmission and incubation delay. Existence and stability of the equilibria have been studied usi...
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doaj-74a3a02c973e4d9db6677830364d94ab2021-04-07T01:10:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-04-0118158359910.3934/mbe.2021032Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmissionFahad Al Basir 0Yasuhiro Takeuchi1Santanu Ray21. Department of Mathematics, Asansol Girls' College, Asansol-4, West Bengal-713304, India2. Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan3. Systems Ecology & Ecological Modelong Laboratory, Department of Zoology, Visva-Bharati University, Santiniketan-731235, IndiaIn the present research, we study a mathematical model for vector-borne plant disease with the plant resistance to disease and vector crowding effect and propose using Beddington-DeAngelis type disease transmission and incubation delay. Existence and stability of the equilibria have been studied using basic reproduction number (R<sub>0</sub>). The region of stability of the different equilibria is presented and the impact of important parameters has been discussed. The results obtained suggest that disease transmission depends on the plant resistance and incubation delay. The delay and resistance rate can stabilise the system and plant epidemic can be avoided increasing plant resistance and incubation period.http://www.aimspress.com/article/doi/10.3934/mbe.2021032?viewType=HTMLmathematical modeldisease resistancecrowding effectincubation periodbasic reproduction numberstabilityhopf bifurcation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Fahad Al Basir Yasuhiro Takeuchi Santanu Ray |
spellingShingle |
Fahad Al Basir Yasuhiro Takeuchi Santanu Ray Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission Mathematical Biosciences and Engineering mathematical model disease resistance crowding effect incubation period basic reproduction number stability hopf bifurcation |
author_facet |
Fahad Al Basir Yasuhiro Takeuchi Santanu Ray |
author_sort |
Fahad Al Basir |
title |
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission |
title_short |
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission |
title_full |
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission |
title_fullStr |
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission |
title_full_unstemmed |
Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission |
title_sort |
dynamics of a delayed plant disease model with beddington-deangelis disease transmission |
publisher |
AIMS Press |
series |
Mathematical Biosciences and Engineering |
issn |
1551-0018 |
publishDate |
2021-04-01 |
description |
In the present research, we study a mathematical model for vector-borne plant disease with the plant resistance to disease and vector crowding effect and propose using Beddington-DeAngelis type disease transmission and incubation delay. Existence and stability of the equilibria have been studied using basic reproduction number (R<sub>0</sub>). The region of stability of the different equilibria is presented and the impact of important parameters has been discussed. The results obtained suggest that disease transmission depends on the plant resistance and incubation delay. The delay and resistance rate can stabilise the system and plant epidemic can be avoided increasing plant resistance and incubation period. |
topic |
mathematical model disease resistance crowding effect incubation period basic reproduction number stability hopf bifurcation |
url |
http://www.aimspress.com/article/doi/10.3934/mbe.2021032?viewType=HTML |
work_keys_str_mv |
AT fahadalbasir dynamicsofadelayedplantdiseasemodelwithbeddingtondeangelisdiseasetransmission AT yasuhirotakeuchi dynamicsofadelayedplantdiseasemodelwithbeddingtondeangelisdiseasetransmission AT santanuray dynamicsofadelayedplantdiseasemodelwithbeddingtondeangelisdiseasetransmission |
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1721537006119419904 |