Fractional Mathematical Model of Covid-19 with Quarantine
This study aims to observe the dynamics of the spread of COVID-19 with the SIR-Model by considering the quarantine (Q) scheme. We also involve a fractional order in the model. Then the basic reproduction numbers were calculated using the generation matrix method, analyzed the local stability of the...
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| Format: | Article |
| Language: | English |
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UIN Syarif Hidayatullah
2022-04-01
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| Series: | InPrime |
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| Online Access: | https://journal.uinjkt.ac.id/index.php/inprime/article/view/23719 |
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| author | Muhammad Rifki Nisardi Kasbawati Kasbawati Khaeruddin Khaeruddin Antonin Robinet Khaled Chetehouna |
| author_facet | Muhammad Rifki Nisardi Kasbawati Kasbawati Khaeruddin Khaeruddin Antonin Robinet Khaled Chetehouna |
| author_sort | Muhammad Rifki Nisardi |
| collection | DOAJ |
| description | This study aims to observe the dynamics of the spread of COVID-19 with the SIR-Model by considering the quarantine (Q) scheme. We also involve a fractional order in the model. Then the basic reproduction numbers were calculated using the generation matrix method, analyzed the local stability of the fractional model for each equilibrium point, and observed its relation to the basic reproduction numbers. We perform the sensitivity analysis to see the effect of parameters on changes in the basic reproduction numbers. We applied the Grunwald-Letnikov method for numerical simulations. Estimation for parameters was also carried out on the existing parameters in the model to obtain parameter values that could represent the actual conditions. Furthermore, with a fractional model, we approximated the model to the data of COVID-19 in West Sulawesi, Indonesia, so that we could obtain a fractional order since it could describe the data more accurately.
Keywords: SIR-Q Model; COVID-19; basic reproduction number; Fractional Mathematical Model; Grunwald Letnikov Method.
Abstrak
Penelitian ini bertujuan untuk mengkaji dinamika penyebaran COVID-19 dengan model matematika orde fraksional penyebaran penyakit SIR-Q dengan mempertimbangkan skema karantina (Q) untuk mengendalikan penyebaran COVID-19. Bilangan reproduksi dasar dihitung menggunakan metode matriks generasi. Kemudian, dianalisa kestabilan lokal model fraksional untuk titik kesetimbangan dan lalu dianalisa kaitannya dengan bilangan reproduksi dasar. Analisis sensitivitas dilakukan untuk mengamati pengaruh parameter terhadap perubahan bilangan reproduksi dasar. Simulasi numerik dilakukan dengan menggunakan metode eksplisit Grunwald-Letnikov. Estimasi juga dilakukan terhadap parameter yang ada pada model untuk memperoleh nilai parameter yang merepresentasikan kondisi aktual penyebaran COVID-19 di Sulawesi Barat. Selanjutnya dengan model fraksional dilakukan pendekatan terhadap data kasus aktif COVID-19 di Sulawesi Barat sehingga diperoleh orde fraksional tertentu yang menghasilkan pendekatan nilai kasus aktif COVID-19 yang lebih akurat terhadap real data.
Kata Kunci: Model SIR-Q; COVID-19; bilangan Reproduksi Dasar; Model Matematika Fraksional; Metode Grunwald-Letnikov. |
| first_indexed | 2024-03-07T20:09:12Z |
| format | Article |
| id | doaj.art-ad70c3aefe9248b1995d30057f998590 |
| institution | Directory Open Access Journal |
| issn | 2686-5335 2716-2478 |
| language | English |
| last_indexed | 2024-03-07T20:09:12Z |
| publishDate | 2022-04-01 |
| publisher | UIN Syarif Hidayatullah |
| record_format | Article |
| series | InPrime |
| spelling | doaj.art-ad70c3aefe9248b1995d30057f9985902024-02-28T02:16:03ZengUIN Syarif HidayatullahInPrime2686-53352716-24782022-04-0141334810.15408/inprime.v4i1.237199086Fractional Mathematical Model of Covid-19 with QuarantineMuhammad Rifki Nisardi0Kasbawati Kasbawati1Khaeruddin Khaeruddin2Antonin Robinet3Khaled Chetehouna4Department of Mathematics, Universitas Hasanuddin, MakassarDepartment of Mathematics, Universitas Hasanuddin, MakassarDepartment of Mathematics, Universitas Hasanuddin, MakassarINSA Centre-Val de Loire, Université d’Orléans, PRISME (EA 4229), BourgesINSA Centre-Val de Loire, Université d’Orléans, PRISME (EA 4229), BourgesThis study aims to observe the dynamics of the spread of COVID-19 with the SIR-Model by considering the quarantine (Q) scheme. We also involve a fractional order in the model. Then the basic reproduction numbers were calculated using the generation matrix method, analyzed the local stability of the fractional model for each equilibrium point, and observed its relation to the basic reproduction numbers. We perform the sensitivity analysis to see the effect of parameters on changes in the basic reproduction numbers. We applied the Grunwald-Letnikov method for numerical simulations. Estimation for parameters was also carried out on the existing parameters in the model to obtain parameter values that could represent the actual conditions. Furthermore, with a fractional model, we approximated the model to the data of COVID-19 in West Sulawesi, Indonesia, so that we could obtain a fractional order since it could describe the data more accurately. Keywords: SIR-Q Model; COVID-19; basic reproduction number; Fractional Mathematical Model; Grunwald Letnikov Method. Abstrak Penelitian ini bertujuan untuk mengkaji dinamika penyebaran COVID-19 dengan model matematika orde fraksional penyebaran penyakit SIR-Q dengan mempertimbangkan skema karantina (Q) untuk mengendalikan penyebaran COVID-19. Bilangan reproduksi dasar dihitung menggunakan metode matriks generasi. Kemudian, dianalisa kestabilan lokal model fraksional untuk titik kesetimbangan dan lalu dianalisa kaitannya dengan bilangan reproduksi dasar. Analisis sensitivitas dilakukan untuk mengamati pengaruh parameter terhadap perubahan bilangan reproduksi dasar. Simulasi numerik dilakukan dengan menggunakan metode eksplisit Grunwald-Letnikov. Estimasi juga dilakukan terhadap parameter yang ada pada model untuk memperoleh nilai parameter yang merepresentasikan kondisi aktual penyebaran COVID-19 di Sulawesi Barat. Selanjutnya dengan model fraksional dilakukan pendekatan terhadap data kasus aktif COVID-19 di Sulawesi Barat sehingga diperoleh orde fraksional tertentu yang menghasilkan pendekatan nilai kasus aktif COVID-19 yang lebih akurat terhadap real data. Kata Kunci: Model SIR-Q; COVID-19; bilangan Reproduksi Dasar; Model Matematika Fraksional; Metode Grunwald-Letnikov.https://journal.uinjkt.ac.id/index.php/inprime/article/view/23719sir-q model, covid-19, basic reproduction number, fractional mathematical modelgrunwald letnikov method. |
| spellingShingle | Muhammad Rifki Nisardi Kasbawati Kasbawati Khaeruddin Khaeruddin Antonin Robinet Khaled Chetehouna Fractional Mathematical Model of Covid-19 with Quarantine InPrime sir-q model, covid-19, basic reproduction number, fractional mathematical model grunwald letnikov method. |
| title | Fractional Mathematical Model of Covid-19 with Quarantine |
| title_full | Fractional Mathematical Model of Covid-19 with Quarantine |
| title_fullStr | Fractional Mathematical Model of Covid-19 with Quarantine |
| title_full_unstemmed | Fractional Mathematical Model of Covid-19 with Quarantine |
| title_short | Fractional Mathematical Model of Covid-19 with Quarantine |
| title_sort | fractional mathematical model of covid 19 with quarantine |
| topic | sir-q model, covid-19, basic reproduction number, fractional mathematical model grunwald letnikov method. |
| url | https://journal.uinjkt.ac.id/index.php/inprime/article/view/23719 |
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