Analisis Kestabilan Model SIR (Susceptible, Infected, Recovered) Dengan Dan Tanpa Vaksinasi

Khusniyah, Sindy Ma'rifatul Ainil (2021) Analisis Kestabilan Model SIR (Susceptible, Infected, Recovered) Dengan Dan Tanpa Vaksinasi. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pandemi merupakan kejadian penyakit pada anggota-anggota suatu populasi tertentu yang terjadi dengan skala penyebaran meliputi daerah geografis yang luas yaitu seluruh negara. Pandemi dapat mengakibatkan kematian yang sangat besar. Salah satu usaha yang dilakukan untuk menanggulangi pandemi yaitu dengan melakukan pemberian vaksinasi. Model epidemi adalah salah satu cara untuk menggambarkan penularan penyakit menular melalui individu. Kemampuan memprediksi penyakit diharapkan dapat memungkinkan para ilmuwan mengevaluasi rencana inokulasi atau isolasi yang selanjutnya akan berpengaruh signifikan terhadap angka kematian suatu pandemi. Oleh karena itu, Tugas Akhir ini bertujuan menganalisis kestabilan model epidemi SIR dengan dan tanpa vaksinasi. Metode yang digunakan pada Tugas Akhir ini meliputi analisis model dan penyusunan simulasi. Model SIR dalam epidemiologi memberikan tiga variabel yaitu jumlah manusia rentan (susceptible), jumlah manusia terinfeksi (infected), dan jumlah manusia sembuh (recovered). Analisis terhadap model dengan mencari titik kesetimbangan kemudian memeriksa kestabilan titik kesetimbangan tersebut. Simulasi numerik diberikan untuk mendukung hasil analisis. Dari hasil analisis model SIR tanpa vaksinasi, diperoleh bilangan reproduksi dasar R_0=β/(γ+μ), simulasi dilakukan ketika R_0 bernilai 0.9 menghasilkan titik kesetimbangan bebas penyakit stabil asimtotik lokal, dan ketika R_0 bernilai 1.5, 1.8, 1.98, 2 titik kesetimbangan endemik stabil asimtotik lokal. Sedangkan hasil analisis model SIR dengan vaksinasi, diperoleh bilangan reproduksi dasar R_v=(β(1-p))/(γ+μ), simulasi dilakukan ketika R_v bernilai 0.792, 0.8 menghasilkan titik kesetimbangan bebas penyakit stabil asimtotik lokal, dan ketika R_v bernilai 1.4 menghasilkan titik kesetimbangan endemik stabil asimtotik lokal. ====================================================================================================== A pandemic is a disease occurrence in members of a certain population that occurs with a scale of spread covering a wide geographical area, namely the entire country. A pandemic can result in very large deaths. One of the efforts made to overcome the pandemic is by giving vaccinations. The epidemic model is one way to describe the transmission of infectious diseases through individuals. The ability to predict disease is expected to allow scientists to evaluate plans for inoculation or isolation which will then have a significant effect on the death rate of a pandemic. Therefore, this final project aims to analyze the stability of the SIR epidemic model with and without vaccination. The method used in this final project includes model analysis and simulation preparation. The SIR model in epidemiology provides three variables, namely the number of susceptible humans (susceptible), the number of infected humans (infected), and the number of recovered humans (recovered). Analysis of the model by finding the equilibrium point and then checking the stability of the equilibrium point. Numerical simulations are provided to support the analysis results. From the analysis of the SIR model without vaccination, the basic reproduction number is R_0=β/(γ+μ), the simulation is carried out when R_0 is 0.9 to produce a locally asymptotically stable disease-free equilibrium point, and when R_0 is 1.5, 1.8, 1.98, 2 equilibrium points locally asymptotically stable endemic. While the results of the analysis of the SIR model with vaccination, the basic reproduction number is R_v=(β(1-p))/(γ+μ), the simulation is carried out when R_v is 0.792, 0.8 produces a local asymptotically stable disease-free equilibrium point, and when R_v is 1.4 produces a locally asymptotically stable endemic equilibrium point.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: analisis kestabilan, model SIR, vaksinasi, titik kesetimbangan, stability analysis, SIR model, vaccination, equilibrium point
Subjects: R Medicine > RZ Other systems of medicine
Divisions: Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User: Sindy Ma’rifatul Ainil Khusniyah
Date Deposited: 26 Aug 2021 06:33
Last Modified: 26 Aug 2021 06:33
URI: https://repository.its.ac.id/id/eprint/89775

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