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Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia

Author

Listed:
  • Wahidah Sanusi
  • Nasiah Badwi
  • Ahmad Zaki
  • Sahlan Sidjara
  • Nurwahidah Sari
  • Muhammad Isbar Pratama
  • Syafruddin Side

Abstract

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 . The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number ; 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.

Suggested Citation

  • Wahidah Sanusi & Nasiah Badwi & Ahmad Zaki & Sahlan Sidjara & Nurwahidah Sari & Muhammad Isbar Pratama & Syafruddin Side, 2021. "Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-8, January.
    • Handle: RePEc:hin:jnljam:2918080
    DOI: 10.1155/2021/2918080
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    Cited by:

    1. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.

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