Model Matematika COVID-19 dengan Sumber Daya Pengobatan yang Terbatas

Utti Marina Rifanti, Atika Ratna Dewi, Nurlaili Nurlaili, Santika Tri Hapsari

Abstract


Coronavirus 2019 (COVID-19) merupakan penyakit menular yang disebabkan oleh Severe Acute Respiratory Syndrome Coronavirus 2. Hingga Desember 2020, terdapat 617 ribu kasus terkonfirmasi positif COVID-19 dengan total 18 ribu kematian karena COVID-19 di Indonesia. Pada penelitian ini, kami menggunakan model kompartemen Susceptible-Exposed-Infected-Recovered (SEIR) untuk analisis dampak sumber daya pengobatan yang terbatas dan memprediksi dinamika penyebaran COVID-19 di Indonesia. Metode yang digunakan adalah penurunan angka rasio reproduksi dasar dan titik ekuilibrium menggunakan analisis sistem dinamik dalam bentuk persamaan diferensial non linier yang diperoleh dari model awal. Kemudian, kami menganalisis angka rasio reproduksi dasar dan titik ekuilibrium, serta memprediksi kondisi pandemi COVID-19 menggunakan kasus nyata di Indonesia sejak 2 Maret hingga 30 Nopember 2020. Dari hasil penelitian ini, diperoleh bahwa jika perubahan kasus terinfeksi  terhadap waktu  kurang dari 2640 kasus, maka angka rasio reproduksi dasar menjadi kurang dari nol dan nilai  semakin mendekati nol saat mulai memasuki bulan Maret 2021. Hal tersebut berarti, jika rata-rata kasus positif terkonfirmasi harian masih di bawah kapasitas maksimal sumber daya pengobatan, yaitu 2640 kasus, maka dari hasil analisis model diprediksikan bahwa penyakit akan mulai menghilang pada bulan Maret 2021. Sebaliknya, jika kasus positif terkonfirmasi harian di atas 2640 kasus, maka diperkirakan penyakit akan mulai menghilang pada Juni 2021.


Keywords


COVID-19; SEIR epidemic model; treatment

Full Text:

PDF

References


T. Hu, Y. Liu, M. Zhao, Q. Zhuang, L. Xu, and Q. He, “A comparison of COVID-19, SARS and MERS,” PeerJ, vol. 8, no. e9725, pp. 1–30, 2020.

World Health Organization, “QA for public,” 2020. [Online]. Available: https://www.who.int/indonesia/news/novel-coronavirus/qa-for-public. [Accessed: 15-Sep-2020].

World Health Organization, “Coronavirus disease 2019 (COVID-19) Situation Report – 73,” Geneva, 2020.

World Health Organization, “WHO Coronavirus Disease (COVID-19) Dashboard,” 2020. [Online]. Available: https://covid19.who.int/table. [Accessed: 15-Sep-2020].

R. Nuraini, “Kasus Covid-19 Pertama, Masyarakat Jangan Panik,” Portal Informasi Indonesia, 2020. [Online]. Available: https://indonesia.go.id/narasi/indonesia-dalam-angka/ekonomi/kasus-covid-19-pertama-masyarakat-jangan-panik. [Accessed: 11-Sep-2020].

K. K. RI, “Daftar Rumah Sakit Rujukan COVID-19 Di Indonesia,” 2020. [Online]. Available: https://infeksiemerging.kemkes.go.id/.

A. Bebey, “Ruang Isolasi Covid-19 Penuh, RSUD Oper Pasien Baru ke Rumah Sakit Lain,” Merdeka.com, 2020. [Online]. Available: https://www.merdeka.com/peristiwa/ruang-isolasi-covid-19-penuh-rsud-oper-pasien-baru-ke-rumah-sakit-lain.html.

M. Gusti, “Kasus Corona Bertambah, Ruang Isolasi RS Rujukan Penuh,” Kompas TV, 2020. [Online]. Available: https://www.kompas.tv/article/130793/kasus-corona-bertambah-ruang-isolasi-rs-rujukan-penuh.

Q. Lin et al., “A conceptual model for the coronavirus disease 2019 ( COVID-19 ) outbreak in Wuhan , China with individual reaction and governmental action,” Int. J. Infect. Dis., vol. 93, no. 2020, pp. 211–216, 2020.

S. Yang et al., “Early estimation of the case fatality rate of COVID-19 in mainland China : a data-driven analysis,” Ann. Transl. Med., vol. 8, no. 4, pp. 6–11, 2020.

N. Chen et al., “Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan , China : a descriptive study,” Lancet, vol. 6736, no. 20, pp. 30211–30217, 2020.

B. Kumar and B. K. Sapra, “A data driven epidemic model to analyse the lockdown effect and predict the course of COVID-19 progress in India,” Chaos, Solitons and Fractals, vol. 139, no. 2020, pp. 1–9, 2020.

A. Mahajan, N. A. Sivadas, and R. Solanki, “An epidemic model SIPHERD and its application for prediction of the spread of COVID-19 infection in India,” Chaos , Solitons Fractals, vol. 140, no. 2020, pp. 1–6, 2020.

Y. Ding and L. Gao, “An evaluation of COVID-19 in Italy : A data-driven modeling analysis,” Infect. Dis. Model., vol. 5, no. 2020, pp. 495–501, 2020.

U. A. De León, Á. G. C. Pérez, and E. Avila-vales, “An SEIARD epidemic model for COVID-19 in Mexico : Mathematical analysis and state-level forecast,” Chaos , Solitons Fractals, vol. 140, no. 2020, pp. 1–23, 2020.

S. Setiati and M. K. Azwar, “COVID-19 and Indonesia,” Acta Medica Indones. – Indones. J. Intern. Med., vol. 52, no. 1, pp. 84–89, 2020.

D. Aldila et al., “A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment : The case of Jakarta , Indonesia,” Chaos, Solitons and Fractals, vol. 139, no. 2020, pp. 1–14, 2020.

E. Soewono, “On the analysis of Covid-19 transmission in Wuhan , Diamond Princess and Jakarta-cluster,” Commun. Biomath. Sci., vol. 3, no. 1, pp. 9–18, 2020.

Z. A. Putra and S. A. Z. Abidin, “Application of SEIR Model in COVID-19 and The Effect of Lockdown on Reducing The Number of Active Cases,” Indones. J. Sci. Technol., vol. 5, no. 2, pp. 185–192, 2020.

W. E. Boyce and R. C. DiPrima, Elementary Differential Equations with Boundary Value Problems, 10th Editi. New Jersey: Prentice-Hall, 2012.

S. A. Al-Sheikh, “Modeling and Analysis of an SEIR Epidemic Model with a Limited Resource for Treatment,” Glob. J. Sci. Front. Res. Math. Decis. Sci., vol. 12, no. 14, pp. 57–66, 2012.

S. COVID-19, “Peta Sebaran COVID-19,” https://covid19.go.id/, 2020. [Online]. Available: https://covid19.go.id/peta-sebaran-covid19.

Bappenas and BPS, “Proyeksi Penduduk Indonesia (Indonesia Population Projection),” Jakarta, 2013.

K. K. RI, “Daftar Rumah Sakit Rujukan COVID-19 Di Indonesia,” kemkes.go.id, 2020. [Online]. Available: https://infeksiemerging.kemkes.go.id/download/Daftar_RS_rujukan_COVID-19.pdf.




DOI: http://dx.doi.org/10.12962/limits.v18i1.8207

Refbacks

  • There are currently no refbacks.


Jumlah Kunjungan:

Creative Commons License
Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/limits.