MODEL STOKASTIK SUSCEPTIBLE INFECTED RECOVERED (SIR)

Yunita, Felin (2013) MODEL STOKASTIK SUSCEPTIBLE INFECTED RECOVERED (SIR). Other thesis, UNIVERSITAS SEBELAS MARET.

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    Abstract

    Felin Yunita. 2013. MODEL STOKASTIK SUSCEPTIBLE INFECTED RECOVERED (SIR). Fakultas Matematika dan Ilmu Pengetahuan Alam. Universitas Sebelas Maret. Model susceptible infected recovered (SIR) menjelaskan penyebaran penyakit dari individu susceptible menjadi infected, kemudian individu infected akan sembuh (recovered) dan tidak terinfeksi kembali karena memiliki kekebalan. Penyebaran penyakit dapat dipandang sebagai kejadian random yang bergantung pada variabel waktu sehingga disebut proses stokastik. Perubahan banyaknya individu susceptible, infected, dan recovered merupakan proses stokastik dalam selang waktu dan variabel random kontinu sehingga dapat dijelaskan dengan model stokastik SIR. Tujuan penulisan ini adalah menurunkan model stokastik SIR. Penyelesaian model stokastik SIR diperoleh dengan formula Ito dan fungsi probabilitas variabel random dari model stokastik SIR harus memenuhi persamaan diferensial Kolmogorov maju. Model stokastik SIR disimulasikan dengan mengambil laju kontak �, laju kesembuhan , dan individu awal yang terinfeksi I(0) yang berbeda. Hasil simulasi menunjukkan bahwa jika semakin besar nilai � maka puncak epidemi semakin tinggi dan semakin besar nilai I(0) maka puncak epidemi juga semakin tinggi. Akan tetapi jika semakin besar nilai maka puncak epidemi semakin rendah. Kata kunci : formula Ito, model SIR, model stokastik, persamaan diferensial Kolmogorov Felin Yunita, 2013. SUSCEPTIBLE INFECTED RECOVERED (SIR) STOCHASTIC MODEL. Faculty of Mathematics and Natural Sciences, Sebelas Maret University. The susceptible infected recovered (SIR) model explains the spread of a disease from the susceptible individuals become infected individuals, then the infected individuals will be recovered and will be not re-infected because they have immunity. The spread of disease is considered as random events which depend on the time variable so it is called a stochastic process. The changes of the number of susceptible, infected, and recovered individuals are a stochastic process with continuous time interval and random variable that can be explained by a SIR stochastic model The purpose of this research is to construct the SIR stochastic model. The solution of the SIR stochastic model is obtained by the Ito formula and the probability function of random variables from the SIR stochastic model must satisfy the Kolmogorov forward differential equations. The SIR stochastic model is simulated by taking the various values of the contact rate �, the recovery rate , and the initial value of infected I(0). The results of simulation show the more value of �, the higher of outbreak, and the more value of I(0), the higher of outbreak. On the other hand the more value of , the lower of outbreak. Key words : Ito formula, Kolmogorov differential equations, SIR model, stochastic model

    Item Type: Thesis (Other)
    Subjects: Q Science > QA Mathematics
    Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika
    Depositing User: Satria Nur Fauzi
    Date Deposited: 19 Apr 2014 05:46
    Last Modified: 19 Apr 2014 05:46
    URI: https://eprints.uns.ac.id/id/eprint/12159

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