Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments
We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/841367 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552405376434176 |
|---|---|
| author | Jianping Wang Shujing Gao Yueli Luo Dehui Xie |
| author_facet | Jianping Wang Shujing Gao Yueli Luo Dehui Xie |
| author_sort | Jianping Wang |
| collection | DOAJ |
| description | We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction number R0 which is defined through the spectral radius of a linear integral operator. If R0 < 1, then the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given. |
| format | Article |
| id | doaj-art-008e8dca6a1a44f6bc1e9047892eaef4 |
| 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-008e8dca6a1a44f6bc1e9047892eaef42025-02-03T05:58:43ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/841367841367Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic EnvironmentsJianping Wang0Shujing Gao1Yueli Luo2Dehui Xie3Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, ChinaKey Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, ChinaKey Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, ChinaKey Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, ChinaWe analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction number R0 which is defined through the spectral radius of a linear integral operator. If R0 < 1, then the disease-free periodic solution is globally asymptotically stable and if R0 > 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.http://dx.doi.org/10.1155/2014/841367 |
| spellingShingle | Jianping Wang Shujing Gao Yueli Luo Dehui Xie Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments Abstract and Applied Analysis |
| title | Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments |
| title_full | Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments |
| title_fullStr | Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments |
| title_full_unstemmed | Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments |
| title_short | Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments |
| title_sort | threshold dynamics of a huanglongbing model with logistic growth in periodic environments |
| url | http://dx.doi.org/10.1155/2014/841367 |
| work_keys_str_mv | AT jianpingwang thresholddynamicsofahuanglongbingmodelwithlogisticgrowthinperiodicenvironments AT shujinggao thresholddynamicsofahuanglongbingmodelwithlogisticgrowthinperiodicenvironments AT yueliluo thresholddynamicsofahuanglongbingmodelwithlogisticgrowthinperiodicenvironments AT dehuixie thresholddynamicsofahuanglongbingmodelwithlogisticgrowthinperiodicenvironments |