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

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 R 0 . The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number R 0 = 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.

Kontrol Optimal Penyebaran Penyakit Demam Berdarah dengan Pengaruh Penyemprotan Insektisida Dan Pengobatan

“…Pada provinsi Sulawesi Selatan kasus demam berdarah pada tahun 2019 terdapat sebanyak 3625 kasus hal ini mengalami kenaikan dari tahun -tahun sebelumnya [2]. Provinsi Sulawesi Selatan merupakan daerah endemik untuk penyakit demam berdarah [3].…”

“…Model matematika ini dirumuskan pada penularan penyakit demam berdarah dalam bentuk non linier sistem persamaan diferensial biasa. Berikut ini adalah model matematika untuk penyebaran penyakit demam berdarah [3].…”

Estimasi Model Penyebaran Penyakit Demam Berdarah dengan Menggunakan Metode Ensemble Kalman Filter

“…Model SIRS demam berdarah diambil dari jurnal Wahidah Sanusi dkk tahun 2021 [5]. Metode yang digunakan untuk mengestimasi model SIRS ini adalah Metode Esemble Kalman Filter yang merupakan pengembangan metode estimasi Kalman Filter [6].…”

“…Dalam model matematika ini dirumuskan pada penularan penyakit demam berdarah dalam bentuk nonlinear sistem persamaan diferensial biasa. Berikut adalah model matematika dari penyebaran penyakit demam berdarah [5]:…”

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

“…In 2021, the authors [21] studied the optimal control strategies through the SEIRS model by considering only the pre-exposure infectious transmission status and the impact of post-reinfection vaccination strategies without regarding the serotype sequence in infection. Sanusi et al [22] studied analyzing a SIRS model and also simulating the model to predict the number of dengue fever cases. The results of the SIRS model for dengue fever can predict the number of dengue cases in South Sulawesi.…”