Indian Journal of Science and Technology
DOI: 10.17485/ijst/2020/v13i03/147852
Year: 2020, Volume: 13, Issue: 3, Pages: 340 – 351
Original Article
Syafruddin Side1,*, Muhammad Isbar Pratama1, Nasiah Badwi2 and Wahidah Sanusi1
1Department of Mathematics, Universitas Negeri Makassar, Parangtambung, Makassar, Indonesia
2Department of Geography, Universitas Negeri Makassar, Parangtambung, Makassar, Indonesia
*Author for correspondence:
Syafruddin Side
Department of Mathematics, Universitas Negeri Makassar, Parangtambung, Makassar, Indonesia
E-mail ID: syafruddin@unm.ac.id
Objectives: The aim of this study is to obtain SIRI model for dengue fever (DHF) transmission, conduct analysis, and simulation of SIRI model in disease-free and endemic and also to predict the number of DHF cases.
Methods/statistical analysis: Dengue fever is caused by a virus carried by the Aedes aegypti and Aedes albopictus mosquitoes, the SIRI model is a modification of the SIR model. Analysis of the SIRI model use the Lyapunov function method, then the data used in the simulation are assuming to show two possible dengue status are disease free and endemic status. The simulation also using the number of dengue case in Makassar city for showing the status of dengue fever transmission in Makassar city. Simulation models using Maple software are to predict the number of dengue cases in the following months.
Findings: The results of this study are the SIRI model of the transmission of dengue fever with variables that have recovered can be re-infected with dengue fever, analysis of the SIRI model of dengue transmission provides information that the equation system in the SIRI model which is asymptotically stable, it means that dengue cases always exist at a certain time and certain region. The simulation results of the SIRI model in this study illustrate the number of dengue cases in the following months. While the first simulation found the basic reproduction number is R0 = 0.0366 ≤ 1 this means that dengue transmission is at an alarming stage, but the second simulation finds the basic reproduction number R0 = 31.2733 > 1, this means that, a person infected with dengue causes eight individuals will be infected with dengue fever, so that it is in the endemic stage, and the last simulation using data of the number of dengue case in Makassar city found = 1, that means, Makassar city is a free disease case for dengue fever transmission.
Application/ improvements: SIRI model for DHF transmission is a mathematical health application. Model analysis guarantees existence, disease-free or endemic status, while simulation results can be used as a reference in DHF prevention.
Keywords: SIRI Model, Dengue Fever, Model Analysis, Simulation, Free Disease, Endemic Dengue.
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