Penyelesaian Model Epidemi Sir Menggunakan Metode Runge-Kutta Orde Empat Dan Metode Adams-Bashforth-Moulton

Setiawan, Laurensius Ian; Mungkasi, Sudi

doi:10.33751/komputasi.v18i2.3623

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…Model epidemi SIR telah banyak diterapkan untuk memprediksi pola perilaku penyakit menyebar pada manusia terhadap waktu dalam suatu daerah. Model SIR juga tersedia dalam bentuk modifikasi yang disesuaikan dengan keadaan yang akan disimulasikan [7]. Modifikasi model yang digunakan pada artikel ini adalah model SEIR karena dapat menggambarkan sifat laten dari penyakit Hepatitis Non HepA-E Akut.…”

Section: Pendahuluanunclassified

Analisis Model Matematika dan Simulasi Pada Penyebaran Hepatitis Non HepA-E Akut di Indonesia

Ristiawan,

Wahyudi,

Selvia

2024

FaktorExacta

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Acute Non-HepA-E Hepatitis is a disease that causes symptoms of severe hepatitis without a definite cause. This research uses literature study methods and information collection to determine assumptions and distribution models, then analyzes the models and carries out numerical simulations. To see the spread of the disease, in this article a mathematical model of the spread of Acute Non-HepA-E Hepatitis is built. The mathematical model is studied analytically and numerical simulations are carried out. Analytical studies are carried out to determine the existence of an equilibrium point and its local stability, as well as to obtain the basic reproduction number 𝑅 0 . By carrying out numerical simulations, information was obtained that to suppress the spread of Acute Non-HepA-E Hepatitis, efforts that can be made are to limit contact between susceptible individuals and individuals who are exposed and infected.

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Section: Pendahuluanunclassified

Analisis Model Matematika dan Simulasi Pada Penyebaran Hepatitis Non HepA-E Akut di Indonesia

Ristiawan,

Wahyudi,

Selvia

2024

FaktorExacta

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“…Adapun solusi yang digunakan untuk memprediksi jumlah penduduk pada penelitian ini menggunakan cara numerik, dengan dua metode yang bisa menuntaskan numerik misalnya metode satu tahap dan metode multi tahap (Fardinah, 2017). Dalam metode satu tahap, cukup membutuhkan suatu nilai awal misalnya metode Runge Kutta sementara beberapa nilai awal dibutuhkan dalam metode multi tahap yang hanya bisa di dapat dari metode satu tahap seperti metode Adam Bashforth Moulton (Setiawan dan Sudi, 2021). Metode Runge-kutta dinyatakan efektif dalam penyelesaian model karena angka galat yang dihasilkan mendekati nilai 0 Suratna dkk, 2023).…”

Section: Pendahuluanunclassified

Persamaan Logistik Menggunakan Metode Adam-Bashforth-Moulton Dalam Memprediksi Jumlah Penduduk Di Indonesia

Sari,

Widyasari,

Cipta

2024

SCI TECH ED MATH

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This study discusses Logistic Equations using the Adam Bashforth Moulton method to predict population growth, which is then solved first with the Runge Kutta method of order-4 to obtain the initial solution then using Adam Bashforth as a predictor and Adam Moulton as a corrector. The logistical equation for population growth with a carrying capacity in Indonesia is K=1,000,000,000 with a step size of h=1, with a growth rate of 1%. Logistics numerical numerical solution with population growth at t=2027 with a step size of h=1 is 274,250,443 people

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Section: Pendahuluanunclassified

Model Matematika pada Penyebaran Penyakit Covid-19 dengan Pengaruh Vaksinasi di DKI Jakarta

Ristiawan,

Solihah

2023

FaktorExacta

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Coronavirus Disease 2019 or Covid-19 is a disease caused by a coronavirus that attacks the respiratory tract causing high fever, cough, flu, shortness of breath, and sore throat. In this paper we formulate a mathematical model of spread of Covid-19 with the effect of vaccination in DKI Jakarta. This model developed the SIR epidemic model into SVIR by adding a population of vaccinated individuals to prevent the spread of Covid-19. The population is divided into four classes: the vulnerable individual class, the vaccinated individual class, the Covid-19 infected individual class, and the recovered individual class. Construction of the models starts by making a flow chart of the spread of Covid-19 with the effect of vaccination. This model obtains two equilibrium points, namely the disease-free equilibrium (𝐸 0 ) point and the endemic equilibrium point (𝐸 * ). Analysis of the system's stability around the equilibrium point gives the primary reproduction number (𝑅 0 ). From the analysis results, the system around the disease-free equilibrium point is (𝐸 0 ) locally asymptotically stable when 𝑅 0 < 1. Then a numerical simulation is carried out to provide a geometric picture related to the results that have been analyzed. The simulation results show that when conditions 𝑅 0 < 1 occur, the disease will disappear, and under conditions 𝑅 0 > 1, the disease will become epidemic. In regards to control strategy in field, this result could give a good understanding of means of slowing down the spread of covid-19.

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Penyelesaian Model Epidemi Sir Menggunakan Metode Runge-Kutta Orde Empat Dan Metode Adams-Bashforth-Moulton

Cited by 3 publications

References 20 publications

Analisis Model Matematika dan Simulasi Pada Penyebaran Hepatitis Non HepA-E Akut di Indonesia

Analisis Model Matematika dan Simulasi Pada Penyebaran Hepatitis Non HepA-E Akut di Indonesia

Persamaan Logistik Menggunakan Metode Adam-Bashforth-Moulton Dalam Memprediksi Jumlah Penduduk Di Indonesia

Model Matematika pada Penyebaran Penyakit Covid-19 dengan Pengaruh Vaksinasi di DKI Jakarta

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