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.
Highlights
The World Health Organization [1] revealed the rapid increase in the number of dengue fever (DF) cases that reached 30 times during the last 50 years
That means South Sulawesi is in the endemic stage of dengue fever
Simulation results using data from the Health Ministry of the Republic of Indonesia show that South Sulawesi is an endemic area of dengue fever; early control and prevention measures need to be done because the climate in Indonesia is increasingly difficult to predict, especially the rainy season which causes many larvae of Aedes mosquitoes spreading dengue virus
Summary
The World Health Organization [1] revealed the rapid increase in the number of dengue fever (DF) cases that reached 30 times during the last 50 years. Considered the most transmitting disease in the world, the DF virus may potentially infect more than half of the world population. Annual data reports [1] show that the number of patients suffering from the DF in hospitals is in the interval of a half to a million people. Dengue fever (DF) is a type of disease in tropical regions, especially Indonesia, including South Sulawesi [1]. The following is the updated DF victims as of 20 January 2016 for several districts/cities in South Sulawesi province: 32 city cases of Makassar, 645 cases of Bone district, 11 cases of Gowa district, 56 cases of Maros district, 125 cases of Pangkep district, 23 cases of Sinjai district, and 225 cases of Luwu district, while other districts/cities have not been recorded [1]
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