### Analisis Model Epidemi SEIR Menggunakan Metode Runge-Kutta Orde 4 pada Penyebaran COVID-19 di Indonesia

Anis Putri Rahmadhani, Ari Kusumastuti, Juhari Juhari

#### Abstract

This study discusses the analysis of the Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model using the fourth-order Runge-Kutta method on the spread of COVID-19 in Indonesia by taking into account the factors limiting community interaction and the percentage of vaccination as model parameters. The purpose of this study was to determine the application of the Susceptible–Exposed–Infected–Recovered (SEIR) model using the fourth-order Runge-Kutta method in dealing with COVID-19 in Indonesia. The steps in analyzing the model are to determine the stability of the model that produces local asymptotic stability, then carry out the implementation as well as simulation using the fourth-order Runge-Kuta method in dealing with COVID-19 in Indonesia. The calculation results show the effect of limiting community interaction and vaccination in reducing cases of COVID-19 infection. Where, when limiting public interaction, the number of cases of COVID-19 infection is lower than before the restrictions on community interaction were carried out, and the higher percentage of vaccinations also resulted in more sloping infection cases. This study provides information that if restrictions on community interaction continue to be carried out by continuing to increase the percentage of vaccinations, it is estimated that the daily graph of positive cases of COVID-19 will be increasingly sloping and close to zero. Thus, the addition of new cases will decrease and it is hoped that the COVID-19 pandemic will end soon.

#### Keywords

SEIR Model of Epidemic; Fourth Order Runge-Kutta Method; COVID-19

PDF

#### References

R. Munir, Metode Numerik, Bandung: Informatika Bandung, 2010.

S. Annas, M. I. Pratama, M. Rifandi, W. Sanusi and S. Side, "Stability Analysis and Numerical Simulation of SEIR Model for Pandemic COVID-19 in Indonesia," Chaos, Solitons and Fractals, vol. 139, no. 110072, pp. 1-7, 2020.

M. Jannah, M. A. Karim and Y. Yulida, "Analisis Kestabilan Model SEIR untuk Penyebaran COVID-19 dengan Parameter Vaksinasi," Jurnal Ilmu Matematika dan Terapan, vol. 3, no. 15, pp. 535-542, 2021.

A. F. Bezabih, G. K. Edessa and P. R. Koya, "Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic," American Journal of Mathematics, vol. 5, no. 6, pp. 247-256, 2020.

C. K. Kwuimy, F. Nazari, X. Jiao, P. Rohani and C.Nataraj, "Nonlinear Dynamic Analysis of an Epidemiological Model for COVID-19 Including Public Behavior and Goverentmen Actions," Nonlinear Dyn, pp. 1545-1559, 2020.

Y. Fang, Y. Nie and M. Penny, "Transmission Dynamics of the COVID‐19 Outbreak and Effectifeness of Goferentmen Interventions: a Data-Driven Analysis," Journal of Medical Virology, vol. 92, no. 10.1002, pp. 645-659, 2020.

Kemenkes, "Peta Sebaran COVID-19," 2021. [Online]. Available: https://covid-19.go.id/. [Accessed 01 September 2021].

K. K. B. P. R. Indonesia, "Siaran Pers Mengenai Penerapan PPKM untuk Mengendalikan Laju Covid-19 dan Menjaga Kehidupan Masyarakat," 21 Juli 2021. [Online]. Available: https://www.ekon.go.id/. [Accessed 02 September 2021].

Kemenkes, "Vaksin COVID-19 Nasional," [Online]. Available: https://vaksin.kemenkes.go.id/. [Accessed 01 September 2021].

C. Y. a. J. Wang, "A mathematical model for the novel coronavirus epidemic in Wuhan, China," Mathematical Biosciences and Enginering, vol. 3, no. 17, pp. 2708-2724, 2020.

H. Wijayanti, S. Setyaningsih and M. Wati, "Metode Runge Kutta dalam Penyelesaian Model Radang Akut," Ekologia, vol. 11, no. 2, pp. 46-52, 2011.

S. Waluya, Persamaan Diferensial, Yogyakarta: Graha Ilmu, 2006.

P. V. d. D. d. P. Watmough, "Reproduction Numbers and Subthreshold Endemic Equilibria for Compartmental Models of Disease," Mathematical Biosciences, Vols. 1-2, no. 180, pp. 29-48, 2002.

P. V. d. Driessche and J. Watmough, "Reproduction Numbers and Subthresold Endemic Equilibria for Compartmental Models of Disease Transmission," Mathematical Biosciences, no. 180, pp. 29-48, 2002.

R. M. McLeod, K. Ranson and L. Biehl, The generalized Riemann integral, JSTOR, 1980.

DOI: https://doi.org/10.18860/jrmm.v2i3.16355

### Refbacks

• There are currently no refbacks.