SIMULASI MODEL EPIDEMI DISCRETE TIME MARKOV CHAIN SUSCEPTIBLE VACCINATED INFECTED SUSCEPTIBLE (DTMC SVIS) PADA POLA PENYEBARAN PENYAKIT INFLUENZA

Hafidh Rifqi Abdullah, Respatiwulan Respatiwulan, Sugiyanto Sugiyanto

Abstract


Abstract: Epidemic models are mathematical model that are built to describe patterns of disease spread. Influenza is an acute respiratory infection that is epidemic worldwide. Influenza disease has a characteristic that provides temporary immunity when recovered. An epidemic model with similar characteristics to influenza is the susceptible infected susceptible (SIS) model. One way to control influenza disease is by vaccination. The SIS epidemic model with vaccination is the susceptible vaccinated infected susceptible (SVIS) epidemic model. There are three groups of individuals in the SVIS epidemic model, namely susceptible (S), vaccinated (V) and infected (I). Changes in the state of susceptible, vaccinated and infected individuals occur randomly in discrete time so that it can be called discrete time markov chain susceptible vaccinated infected susceptible (DTMC SVIS). The purpose of this study is to modify the SIS model by adding a vaccinated group and simulate it in influenza disease. The simulation is made by modifying several parameter values. The simulation results of the DTMC SVIS model show that increasing the vaccination rate parameter cannot significantly reduce the number of influenza infections. The spread of influenza disease can be prevented by reducing the transmission rate parameter.
 Abstrak: Model epidemi adalah pemodelan matematika yang dibangun untuk menggambarkan pola penyebaran penyakit. Influenza adalah infeksi saluran pernapasan akut yang menjadi epidemi di seluruh dunia. Penyakit influenza memiliki karakteristik yaitu memberikan kekebalan sementara pada saat sembuh. Model epidemi yang berkarakteristik serupa dengan influenza adalah model susceptible infected susceptible (SIS). Salah satu cara pengendalian penyakit influenza dengan pemberian vaksinasi. Model epidemi SIS dengan pemberian vaksinasi adalah model epidemi susceptible vaccinated infected susceptible (SVIS). Terdapat tiga kelompok individu dalam model epidemi SVIS yaitu susceptible (S), vaccinated (V) dan infected (I). Perubahan state individu susceptible, vaccinated, dan infected terjadi secara random dalam waktu diskrit sehingga dapat disebut discrete time markov chain susceptible vaccinated infected susceptible (DTMC SVIS). Tujuan penelitian ini adalah memodifikasi model SIS dengan menambah kelompok vaccinated dan mensimulasikannya pada penyakit influenza. Simulasi dibuat dengan modifikasi beberapa nilai parameter. Hasil simulasi model DTMC SVIS menunjukkan bahwa peningkatan parameter laju vaksinasi tidak dapat menurunkan angka infeksi influenza secara signifikan. Penyebaran penyakit influenza dapat dicegah dengan mengurangi parameter laju penularan.

Keywords


Model Epidemi; SVIS; Vaksinasi; Influenza

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