Threshold dynamics of a time periodic and two–group epidemic model with distributed delay
In this paper, a time periodic and two–group reaction–diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-09-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017080 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590063111766016 |
|---|---|
| author | Lin Zhao Zhi-Cheng Wang Liang Zhang |
| author_facet | Lin Zhao Zhi-Cheng Wang Liang Zhang |
| author_sort | Lin Zhao |
| collection | DOAJ |
| description | In this paper, a time periodic and two–group reaction–diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of $R_0$, that is, the disease is uniformly persistent if $R_0 \gt 1$, while the disease goes to extinction if $R_0 \lt 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio–temporal variables. |
| format | Article |
| id | doaj-art-894f2e4cbfbf4c028f0a0dbdc6226ef7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-894f2e4cbfbf4c028f0a0dbdc6226ef72025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61535156310.3934/mbe.2017080Threshold dynamics of a time periodic and two–group epidemic model with distributed delayLin Zhao0Zhi-Cheng Wang1Liang Zhang2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaIn this paper, a time periodic and two–group reaction–diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of $R_0$, that is, the disease is uniformly persistent if $R_0 \gt 1$, while the disease goes to extinction if $R_0 \lt 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio–temporal variables.https://www.aimspress.com/article/doi/10.3934/mbe.2017080two–group epidemic modeltime periodicdistributed delaythreshold dynamicslyapunov functional |
| spellingShingle | Lin Zhao Zhi-Cheng Wang Liang Zhang Threshold dynamics of a time periodic and two–group epidemic model with distributed delay Mathematical Biosciences and Engineering two–group epidemic model time periodic distributed delay threshold dynamics lyapunov functional |
| title | Threshold dynamics of a time periodic and two–group epidemic model with distributed delay |
| title_full | Threshold dynamics of a time periodic and two–group epidemic model with distributed delay |
| title_fullStr | Threshold dynamics of a time periodic and two–group epidemic model with distributed delay |
| title_full_unstemmed | Threshold dynamics of a time periodic and two–group epidemic model with distributed delay |
| title_short | Threshold dynamics of a time periodic and two–group epidemic model with distributed delay |
| title_sort | threshold dynamics of a time periodic and two group epidemic model with distributed delay |
| topic | two–group epidemic model time periodic distributed delay threshold dynamics lyapunov functional |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017080 |
| work_keys_str_mv | AT linzhao thresholddynamicsofatimeperiodicandtwogroupepidemicmodelwithdistributeddelay AT zhichengwang thresholddynamicsofatimeperiodicandtwogroupepidemicmodelwithdistributeddelay AT liangzhang thresholddynamicsofatimeperiodicandtwogroupepidemicmodelwithdistributeddelay |