Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age
Abstract This study discusses the behavioral analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population of measles is grouped into four age groups, namely the first age group (0-4 years), the second age group (5-9 years),...
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| Format: | Article |
| Language: | English |
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UIN Syarif Hidayatullah
2023-11-01
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| Series: | InPrime |
| Subjects: | |
| Online Access: | https://journal.uinjkt.ac.id/index.php/inprime/article/view/32318 |
| _version_ | 1827339926520201216 |
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| author | Juhari Juhari Olivia Karinina Abdul Aziz Evawati Alisah |
| author_facet | Juhari Juhari Olivia Karinina Abdul Aziz Evawati Alisah |
| author_sort | Juhari Juhari |
| collection | DOAJ |
| description | Abstract
This study discusses the behavioral analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population of measles is grouped into four age groups, namely the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years) and the fourth age group (> 15 years). The steps in modeling behavior can be done by determining the equilibrium point, and the basic reproduction number and performing a global stability analysis by building the Lyapunov function. This research contributes to providing information both to the government and the community.
Keywords: Epidemic Model; SIR; Lyapunov function; Measles.
Abstrak
Penelitian ini membahas model analisis perilaku epidemi Susceptible-Infected-Recovered (SIR) penyebaran campak berdasarkan struktur umur. Jumlah penduduk yang terkena campak dikelompokkan menjadi empat kelompok umur, yaitu kelompok umur pertama (0-4 tahun), kelompok umur kedua (5-9 tahun), kelompok umur ketiga (10-14 tahun) dan kelompok umur keempat. (> 15 tahun). Langkah-langkah dalam pemodelan perilaku dapat dilakukan dengan menentukan titik ekuilibrium, bilangan reproduksi dasar dan melakukan analisis stabilitas global dengan membangun fungsi Lyapunov. Penelitian ini memberikan kontribusi untuk memberikan informasi baik kepada pemerintah maupun masyarakat.
Kata Kunci: Model Epidemi; PAK; fungsi Lyapunov; Campak.
2020MSC: 00A71. |
| first_indexed | 2024-03-07T20:08:43Z |
| format | Article |
| id | doaj.art-2513ebf5d7fe4b36a2305a011b1a6a34 |
| institution | Directory Open Access Journal |
| issn | 2686-5335 2716-2478 |
| language | English |
| last_indexed | 2024-03-07T20:08:43Z |
| publishDate | 2023-11-01 |
| publisher | UIN Syarif Hidayatullah |
| record_format | Article |
| series | InPrime |
| spelling | doaj.art-2513ebf5d7fe4b36a2305a011b1a6a342024-02-28T02:16:03ZengUIN Syarif HidayatullahInPrime2686-53352716-24782023-11-015214416010.15408/inprime.v5i2.3231811477Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on AgeJuhari Juhari0Olivia Karinina1Abdul Aziz2Evawati Alisah3Department of Mathematics, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Malang,Department of Mathematics, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Malang,Department of Mathematics, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Malang,Department of Mathematics, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Malang,Abstract This study discusses the behavioral analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population of measles is grouped into four age groups, namely the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years) and the fourth age group (> 15 years). The steps in modeling behavior can be done by determining the equilibrium point, and the basic reproduction number and performing a global stability analysis by building the Lyapunov function. This research contributes to providing information both to the government and the community. Keywords: Epidemic Model; SIR; Lyapunov function; Measles. Abstrak Penelitian ini membahas model analisis perilaku epidemi Susceptible-Infected-Recovered (SIR) penyebaran campak berdasarkan struktur umur. Jumlah penduduk yang terkena campak dikelompokkan menjadi empat kelompok umur, yaitu kelompok umur pertama (0-4 tahun), kelompok umur kedua (5-9 tahun), kelompok umur ketiga (10-14 tahun) dan kelompok umur keempat. (> 15 tahun). Langkah-langkah dalam pemodelan perilaku dapat dilakukan dengan menentukan titik ekuilibrium, bilangan reproduksi dasar dan melakukan analisis stabilitas global dengan membangun fungsi Lyapunov. Penelitian ini memberikan kontribusi untuk memberikan informasi baik kepada pemerintah maupun masyarakat. Kata Kunci: Model Epidemi; PAK; fungsi Lyapunov; Campak. 2020MSC: 00A71.https://journal.uinjkt.ac.id/index.php/inprime/article/view/32318epidemic modelsirlyapunov functionmeasles |
| spellingShingle | Juhari Juhari Olivia Karinina Abdul Aziz Evawati Alisah Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age InPrime epidemic model sir lyapunov function measles |
| title | Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age |
| title_full | Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age |
| title_fullStr | Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age |
| title_full_unstemmed | Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age |
| title_short | Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age |
| title_sort | global stability analysis of susceptible infected recovered s i r model measles vaccination based on age |
| topic | epidemic model sir lyapunov function measles |
| url | https://journal.uinjkt.ac.id/index.php/inprime/article/view/32318 |
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