ANALISIS SENSITIVITAS DAN KONTROL OPTIMAL MODEL SEIR PENYEBARAN COVID-19 DI INDONESIA
DOI:
https://doi.org/10.24114/jmk.v7i3.32461Keywords:
Sensitivitas, Kontrol Optimal, Model SEIR, Covid-19Abstract
” Covid-19 (Coronavirus Disease) merupakan penyakit yang menyerang sistem pernafasan akibat infeksi SARS-CoV-2 (Severe Acute Respiratory Syndrome 2). Wabah ini ditemukan pertama kali di Wuhan, provinsi Hubei, Cina pada Desember 2019 dan menyebar dengan cepat ke berbagai negara sehingga dinyatakan sebagai pandemi pada Maret 2020. Sebagai upaya mengatasi pandemi Covid-19, ilmuwan matematika mengembangkan berbagai model matematika untuk mempelajari karakteristik epidemi wabah, memprediksi penyebaran virus serta menawarkan berbagai langkah intervensi. Penelitian ini bertujuan untuk menganalisis sensitvitas dan kontrol optimal dari model SEIR penyebaran Covid-19 dengan menerapkan strategi kontrol berupa vaksinasi individu rentan dan pengobatan individu terinfeksi. Hasil analisis sensitivitas menunjukkan bahwa parameter terkait penambahan jumlah individu rentan dan kematian individu rentan merupakan parameter paling berpengaruh terhadap nilai bilangan reproduksi dasar, jumlah individu terpapar dan terinfeksi. Penerapan strategi kontrol pada model berupa vaksinasi dan pengobatan penting untuk dilakukan karena efektif untuk menurunkan jumlah individu terinfeksi hingga 99%. Covid-19 (Coronavirus Disease) is an acute respiratory system disease caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome 2). This outbreak was first discovered in Wuhan, Hubei province, China in December 2019 and has spread rapidly to various countries and was declared as a pandemic in March 2020. To overcome the Covid-19 pandemic, mathematicians develop mathematical model to study the spread of viruses and offer various intervention measures. This study aims to analyze the sensitivity and optimal control of the SEIR model for the Covid-19 dynamic in Indonesia by implementing control strategies. The control strategy used is vaccination of susceptible individuals and treatment of infected individuals. The sensitivity analysis shows that the rate of increase in the number of susceptible individuals and the mortality of susceptible individuals is the parameter that most influences the value of the basic reproduction number, the number of exposed and infected individuals. The control strategy used was effective in reducing the number of infected individuals to aroud 99%.References
H. Ouassou, L. Kharchoufa, M. Bouhrim, N. E. Daoudi, H. Imtara, N. Bencheikh, A. Elbouzidi dan M. Bnouham, œThe pathogenesis of coronavirus disease 2019 (Covid-19): Evaluation and prevention, Journal of Immunoogy Research, vol. 2020, pp. 1-7, 2020.
World Healt Organization. (2021) WHO Coronavirus Disease (Covid-19) Dashboard [Online]. Available: https://covid19.who.int
Kementerian Kesehatan Republik Indonesia. (2021) Situasi Covid-19 di Indonesia [Online]. Available: https://covid19.go.id.
A. Zeb, E. Alzahrani, V. S. Erturk dan G. Zaman, œMathematical model for coronavirus disease 2019 (Covid-19) containing isolation class, BioMed Research International, vol. 2020, pp. 1-7, 2020.
J. Jiao, Z. Liu dan S. Chai, œDynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible, Applied Mathematics Letters, vol. 107, pp. 1-7, 2020.
S. Annas, M. I. Pratama, M. Rifandi, W. Sanusi dan S. Side, œStability analysis and numerical simulation of SEIR model for pandemic Covid-19 spread in Indonesia, Chaos, Solitons and Fractals, vol. 139, pp. 1-17, 2020.
S. Mandal, T. Bhatnagar, N. Arinaminpathy, A. Agarwal, A. Chowdhury, M. Murhekar, R. R. Gangakhedkar dan S. Sarkar, œPrudent public health intervention strategies to control the coronavirus disease-2019 transmission in India: a mathematical model-based approach, India J Med Res, vol. 151, pp. 190-199, 2020.
Rustam dan L. Handayani, œThe outbreaks modelling of coronavirus (Covid-19) using the modified SEIR model in Indonesia, SPEKTRA: Jurnal Fisika dan Aplikasinya, vol. 5, pp. 61-68, 2020.
F. Ndairou, I. Area, J. J. Nieto dan F. M. Torres, œMathematical modelling of Covid-19 transmission dynamics with a case study of Wuhan, Chaos, Solitons and Fractals, vol. 135, pp. 1-11, 2020.
K. Lee, J. Kim dan H. Kwon, œOptimal control of an influenza model with seasonal forcing and age-dependent transmission rate, Journal of Theoretical Biology, vol. 317, pp. 310-320, 2013.
Subchan, I. Fitria dan A. M. Syafi™i, œAn epidemic cholera model with control treatment and intervention, Journal of Physics: Conference Series, vol. 1218, pp. 1-9, 2019.
T. Hussain, M. Ozair, F. Ali, S. Rehman, T. A. Assiri dan E. E. Mahmoud, œSensitivity analysis and optimal control of Covid-19 dynamics based on SEIQR model, Results in Physics, vol. 22, pp. 1-11, 2021.
C. E. Madubueze, S. Dachollom dan I. O. Onwubuya, œControlling the spread of Covid-19: Optimal control analysis, Computation and Mathematical Methods in Medicine, vol. 2020, pp. 1-4, 2020.
L. P. Sinaga, H. Nasution dan D. Kartika, œStability analysis of the corona virus (Covid-19) dynamics SEIR model in Indonesia, Journal of Physics: Conference Series, vol. 189, pp: 1-9, 2021.
P. Driessche and J. Watmough, œReproduction numbers and sub-treshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, vol. 180, pp: 29-48, 2002.
P. N. V. Tu, Introductory Optimization Dynamics: Optimum Control with Economins and Management Applications. New York: Springer-Verlag, 1984.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Penulis.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (Refer to The Effect of Open Access).
