Analisis dan simulasi stokastik model penularan penyakit COVID-19 di India dengan asimtomatik, karantina, vaksinasi, dan mutasi virus

Angelina, Grace (2022) Analisis dan simulasi stokastik model penularan penyakit COVID-19 di India dengan asimtomatik, karantina, vaksinasi, dan mutasi virus. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Penelitian ini memodelkan penularan penyakit COVID-19 dengan mengembangkan model epidemi SIR klasik dengan penambahan kompartemen asimtomatik, vaksinasi, karantina, dan meninggal yang disebut sebagai model epidemi SVIQDR. Model epidemi SVIQDR ini juga akan diteliti sebelum adanya vaksinasi dimana k,σ,V=0 menjadi model epidemi SIQDR. Kemudian, akan dilakukan analisis model matematika tersebut dengan mencari titik ekuilibrium dan bilangan reproduksi dasar (R0) dari kedua model tersebut. Selanjutnya, dengan menggunakan nilai parameter yang menyesuaikan situasi di India, akan dilakukan juga analisis terhadap titik ekuilibrium dan bilangan reproduksi dasar. Model ini akan disimulasikan menggunakan R-Studio dengan nilai parameter yang menyesuaikan situasi ada di India pada tanggal 30 Januari 2021 hingga 30 September 2022. Simulasi yang dilakukan terdiri dari 3 buah simulasi yaitu; sebelum vaksinasi, setelah vaksinasi, dan setelah mutasi virus. Mutasi virus menjadi penyebab adanya gelombang kedua pandemi penyakit COVID-19 di India disimulasikan pada waktu yang berbeda dengan nilai laju penularan yang lebih besar. Simulasi stokastik dilakukan dengan cara mensimulasikan 700 buah nilai laju penularan yang berdistribusi gamma dimana 700 buah simulasi adalah jumlah simulasi yang stabil, lalu hasil simulasi merupakan hasil rata-rata dari 700 buah hasil simulasi. Hasil dari simulasi ini dihitung akurasi dengan data asli kasus baru di India menggunakan metode mean absolute error (MAE) diperoleh nilai sebesar 16.660 individu. Agar dapat menurunkan laju penularan penyakit COVID-19, perlu dilakukan pembatasan sosial dan vaksinasi. / This study modeled the transmission of COVID-19 disease by developing a classic SIR epidemic model with the addition compartments such as asymptomatic, vaccination, quarantine, and death known as the SVIQDR epidemic model. This SVIQDR epidemic model will also be studied before vaccination where k,σ,V=0 becomes the SIQDR epidemic model. Then, an analysis of the mathematical model will be carried out by finding the equilibrium point and the basic reproduction number (R0) of the two models. Furthermore, by using parameter values that adapt to the situation in India, an analysis of the equilibrium point and basic reproduction numbers will also be carried out. This model will be simulated using R-Studio with parameter values that adjust the situation in India from January 30, 2021 to September 30, 2022. The simulation consists of 3 simulations namely; before vaccination, after vaccination, and after virus mutation. The virus mutation that caused the second wave of the COVID-19 pandemic in India was simulated at a different time with a higher transmission rate. The stochastic simulation is carried out by simulating 700 transmission rate values with a gamma distribution where 700 simulations is a stable number of simulations, then the simulation results are the average results of 700 simulation results. The results of this simulation are calculated for accuracy with the original data of new cases in India using the mean absolute error (MAE) method, obtaining a value of 16,660 individuals. In order to reduce the rate of transmission of the COVID-19 disease, it is necessary to implement social restrictions and vaccination.

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