Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina

Resmawan Resmawan, Agusyarif Rezka Nuha, Lailany Yahya



Makalah ini membahas dinamika transmisi COVID-19 dengan melibatkan intervensi karantina. Model dikonstruksi dengan melibatkan tiga kelas penyebab infeksi, yaitu kelas manusia terpapar, kelas manusia terinfeksi tanpa gejala klinis, dan kelas manusia terinfeksi disertai gejala klinis. Variabel yang merepresentasikan intervensi karantina untuk menekan pertumbuhan infeksi juga dipertimbangkan pada model. Selanjutnya, analisis model difokuskan pada eksistensi titik kesetimbangan dan simulasi numerik untuk menunjukkan dinamika populasi secara visual. Model yang dikonstruksi membentuk model SEAQIR yang memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal pada saat R0<1 dan tidak stabil pada saat R0>1. Simulasi numerik menunjukkan bahwa peningkatan intervensi berupa karantina dapat berkontribusi memperlambat transmisi COVID-19 sehingga diharapkan dapat mencegah terjadinya wabah pada populasi.


This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R0<1 and unstable at R0>1. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.


Dynamic Analysis; COVID-19 Transmission; Equilibrium Point; Quarantine

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N. Al-Rousan and H. Al-Najjar, “The correlation between the spread of COVID-19 infections and weather variables in 30 Chinese provinces and the impact of Chinese government mitigation plans,” Eur Rev Med Pharmacol Sci, vol. 24, no. 8, pp. 4565–4571, 2020.

C. Huang et al., “Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China,” Lancet, vol. 395, no. 10223, pp. 497–506, Feb. 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. 395, no. 10223, pp. 507–513, Feb. 2020.

R. Lu et al., “Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding,” Lancet, vol. 395, no. 10224, pp. 565–574, Feb. 2020.

T. Li, “Diagnosis and clinical management of severe acute respiratory syndrome Coronavirus 2 (SARS-CoV-2) infection: an operational recommendation of Peking Union Medical College Hospital (V2.0),” Emerg. Microbes Infect., vol. 9, no. 1, pp. 582–585, Jan. 2020.

M. Li et al., “Identifying novel factors associated with COVID-19 transmission and fatality using the machine learning approach,” Sci. Total Environ., p. 142810, Oct. 2020.

B. Tang et al., “Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions,” J. Clin. Med., vol. 9, no. 2, p. 462, Feb. 2020.

B. Tang, N. L. Bragazzi, Q. Li, S. Tang, Y. Xiao, and J. Wu, “An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov),” Infect. Dis. Model., vol. 5, pp. 248–255, 2020.

B. Tang et al., “The effectiveness of quarantine and isolation determine the trend of the COVID-19 epidemics in the final phase of the current outbreak in China,” Int. J. Infect. Dis., vol. 95, pp. 288–293, Jun. 2020.

M. A. Khan and A. Atangana, “Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative,” Alexandria Eng. J., vol. 59, no. 4, pp. 2379–2389, Aug. 2020.

M. A. Khan and A. Atangana, “Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative,” Alexandria Eng. J., 2020.

T.-M. Chen, J. Rui, Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui, and L. Yin, “A mathematical model for simulating the phase-based transmissibility of a novel coronavirus,” Infect. Dis. Poverty, vol. 9, no. 1, p. 24, Dec. 2020.

T. Kuniya, “Prediction of the Epidemic Peak of Coronavirus Disease in Japan, 2020,” J. Clin. Med., vol. 9, no. 3, p. 789, Mar. 2020.

H. Sun, Y. Qiu, H. Yan, Y. Huang, Y. Zhu, and S. X. Chen, “Tracking and Predicting COVID-19 Epidemic in China Mainland,” J. Data Sci., vol. 18, no. 3, pp. 455–472, 2020.

C. T. Deressa and G. F. Duressa, “Modeling and optimal control analysis of transmission dynamics of COVID-19: The case of Ethiopia,” Alexandria Eng. J., vol. 60, no. 1, pp. 719–732, Feb. 2021.

D. Kada, A. Kouidere, O. Balatif, M. Rachik, and E. H. Labriji, “Mathematical modeling of the spread of COVID-19 among different age groups in Morocco: Optimal control approach for intervention strategies,” Chaos, Solitons & Fractals, vol. 141, p. 110437, Dec. 2020.

B. Tang et al., “Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions,” J. Clin. Med., vol. 9, no. 2, p. 462, 2020.

P. Li et al., “Transmission of COVID-19 in the terminal stages of the incubation period: A familial cluster,” Int. J. Infect. Dis., vol. 96, no. February, pp. 452–453, 2020.

R. Resmawan and L. Yahya, “Sensitivity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission,” CAUCHY, vol. 6, no. 2, pp. 91–99, May 2020.

P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, no. 1–2, pp. 29–48, Nov. 2002.

S. Fisher, Complex Variables. California (US): Wadsworth & Brooks, 1990.


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