Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia
This study is aimed at building and analysing a SIRS model and also simulating the model to predict the number of dengue fever cases. Methods applied for this model are building the SIRS model by modifying the SIR model, analysing the SIRS model using the Lyapunov function to prove three theorems (t...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2918080 |
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| author | Wahidah Sanusi Nasiah Badwi Ahmad Zaki Sahlan Sidjara Nurwahidah Sari Muhammad Isbar Pratama Syafruddin Side |
| author_facet | Wahidah Sanusi Nasiah Badwi Ahmad Zaki Sahlan Sidjara Nurwahidah Sari Muhammad Isbar Pratama Syafruddin Side |
| author_sort | Wahidah Sanusi |
| collection | DOAJ |
| description | This study is aimed at building and analysing a SIRS model and also simulating the model to predict the number of dengue fever cases. Methods applied for this model are building the SIRS model by modifying the SIR model, analysing the SIRS model using the Lyapunov function to prove three theorems (the existence, the free disease, and the endemic status of dengue fever), and simulating the SIRS model using the number of dengue case data in South Sulawesi by Maple. The results obtained are the SIRS model of dengue fever transmission, stability analysis, global stability, and the value of the basic reproduction number R0. The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number R0=26.47609>1; it means that South Sulawesi is in the endemic stage of transmission for dengue fever disease. Simulation of the SIRS model for dengue fever can predict the number of dengue cases in South Sulawesi that could be a recommendation for the government in an effort to prevent the number of dengue fever cases. |
| format | Article |
| id | doaj-art-7d7c1da5fcfc4228832a58ffcd387104 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7d7c1da5fcfc4228832a58ffcd3871042025-02-03T01:05:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/29180802918080Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, IndonesiaWahidah Sanusi0Nasiah Badwi1Ahmad Zaki2Sahlan Sidjara3Nurwahidah Sari4Muhammad Isbar Pratama5Syafruddin Side6Mathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaGeography Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaMathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaMathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaMathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaMathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaMathematics Department, Universitas Negeri Makassar, Makassar 90222, IndonesiaThis study is aimed at building and analysing a SIRS model and also simulating the model to predict the number of dengue fever cases. Methods applied for this model are building the SIRS model by modifying the SIR model, analysing the SIRS model using the Lyapunov function to prove three theorems (the existence, the free disease, and the endemic status of dengue fever), and simulating the SIRS model using the number of dengue case data in South Sulawesi by Maple. The results obtained are the SIRS model of dengue fever transmission, stability analysis, global stability, and the value of the basic reproduction number R0. The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number R0=26.47609>1; it means that South Sulawesi is in the endemic stage of transmission for dengue fever disease. Simulation of the SIRS model for dengue fever can predict the number of dengue cases in South Sulawesi that could be a recommendation for the government in an effort to prevent the number of dengue fever cases.http://dx.doi.org/10.1155/2021/2918080 |
| spellingShingle | Wahidah Sanusi Nasiah Badwi Ahmad Zaki Sahlan Sidjara Nurwahidah Sari Muhammad Isbar Pratama Syafruddin Side Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia Journal of Applied Mathematics |
| title | Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia |
| title_full | Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia |
| title_fullStr | Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia |
| title_full_unstemmed | Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia |
| title_short | Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia |
| title_sort | analysis and simulation of sirs model for dengue fever transmission in south sulawesi indonesia |
| url | http://dx.doi.org/10.1155/2021/2918080 |
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