Abstract
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.
Highlights
Introduction he World HealthOrganization [1] states that the number of dengue fever (DHF) cases in the world has increased 30-fold over the past 50 years, and was named the fastest growing disease in the world and more than half of the world’s research results are related quality
The SIRI model simulation by using Maple with initial and parameter values based on the assumptions is presented in Table 2, with basic reproduction number values obtained based on equation (9), namely:
While the basic reproduction number for dengue fever foun= d R0 0.0272 < 1, this means that infected individuals cannot transmit to other individuals in Makassar city that cause the disease to disappear from the population or the stage of DHF in Makassar city, South Sulawesi Indonesia is free disease case
Summary
Organization [1] states that the number of dengue fever (DHF) cases in the world has increased 30-fold over the past 50 years, and was named the fastest growing disease in the world and more than half of the world’s research results are related quality. Data from around the world [1] show that Asia determines the first place in the number of dengue fever patients each year. Starting in 1968 until 2016, Indonesia was the highest country with Dengue Fever in Southeast Asia [1]. Makassar city is one of the districts in South Sulawesi with the highest number of dengue cases. According to the Health Department Makassar City, the number of dengue cases in Makassar in 2016 is 142 cases, 2017 is 248 cases and January to February 2018 is 62 cases [2]
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