Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment
Abstract Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquito-borne epidemic model by incorporating mosquitoes’ aquatic stage (eggs, larvae, a...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02807-6 |
| _version_ | 1819265092217208832 |
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| author | Ting-Ting Zheng Lin-Fei Nie Zhidong Teng Yantao Luo |
| author_facet | Ting-Ting Zheng Lin-Fei Nie Zhidong Teng Yantao Luo |
| author_sort | Ting-Ting Zheng |
| collection | DOAJ |
| description | Abstract Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquito-borne epidemic model by incorporating mosquitoes’ aquatic stage (eggs, larvae, and pupae) and seasonal shift factor, which is a periodic discontinuous differential system. Firstly, some sufficient conditions for the existence and uniqueness of a disease-free solution are obtained. Further, we define the basic reproduction number R 0 $\mathcal{R}_{0}$ , and obtain the stability of the disease-free solution when R 0 $\mathcal{R}_{0}$ is less than one. And, if R 0 $\mathcal{R}_{0}$ is greater than one, the mosquito-borne disease is uniformly persistent and the model admits a positive periodic solution. Finally, some numerical simulations are given to illustrate the main theoretical results. In addition, simulation results also imply that ignoring the effects of seasonal succession can overestimate or underestimate mosquito-borne disease trends. |
| first_indexed | 2024-12-23T20:39:53Z |
| format | Article |
| id | doaj.art-28a20e88195e42c6a56ace789205aa39 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T20:39:53Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-28a20e88195e42c6a56ace789205aa392022-12-21T17:31:57ZengSpringerOpenAdvances in Difference Equations1687-18472020-09-012020111610.1186/s13662-020-02807-6Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environmentTing-Ting Zheng0Lin-Fei Nie1Zhidong Teng2Yantao Luo3College of Mathematics and Systems Science, Xinjiang UniversityCollege of Mathematics and Systems Science, Xinjiang UniversityCollege of Mathematics and Systems Science, Xinjiang UniversityCollege of Mathematics and Systems Science, Xinjiang UniversityAbstract Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquito-borne epidemic model by incorporating mosquitoes’ aquatic stage (eggs, larvae, and pupae) and seasonal shift factor, which is a periodic discontinuous differential system. Firstly, some sufficient conditions for the existence and uniqueness of a disease-free solution are obtained. Further, we define the basic reproduction number R 0 $\mathcal{R}_{0}$ , and obtain the stability of the disease-free solution when R 0 $\mathcal{R}_{0}$ is less than one. And, if R 0 $\mathcal{R}_{0}$ is greater than one, the mosquito-borne disease is uniformly persistent and the model admits a positive periodic solution. Finally, some numerical simulations are given to illustrate the main theoretical results. In addition, simulation results also imply that ignoring the effects of seasonal succession can overestimate or underestimate mosquito-borne disease trends.http://link.springer.com/article/10.1186/s13662-020-02807-6Mosquito-borne diseaseSeasonal variationPeriodic solutionStability and persistence |
| spellingShingle | Ting-Ting Zheng Lin-Fei Nie Zhidong Teng Yantao Luo Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment Advances in Difference Equations Mosquito-borne disease Seasonal variation Periodic solution Stability and persistence |
| title | Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment |
| title_full | Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment |
| title_fullStr | Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment |
| title_full_unstemmed | Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment |
| title_short | Modeling seasonal variation for mosquito-borne disease in the tropical monsoon environment |
| title_sort | modeling seasonal variation for mosquito borne disease in the tropical monsoon environment |
| topic | Mosquito-borne disease Seasonal variation Periodic solution Stability and persistence |
| url | http://link.springer.com/article/10.1186/s13662-020-02807-6 |
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