Analisis Dinamik Model Penyebaran COVID-19 dengan Vaksinasi

Resmawan Resmawan, Lailany Yahya, Revandi S. Pakaya, Hasan S. Panigoro, Agusyarif Rezka Nuha

Abstract


Coronavirus Disease 2019 (COVID-19) is a new type of virus from a large family of viruses transmitted between humans and animals (zoonotically transmitted) that was first discovered in Wuhan City, Hubei Province, China in late 2019 which is still widespread and threat throughout the world including Indonesia. This article discussed about the mathematical model of the spread of COVID-19 with vaccinations. In this case, the human population is divided into 5 classes, namely the suspected, vaccine, exposed, infected and recovered classes. The constructed model forms an SVEIR model that has two equilibrium points, namely disease-free and endemic equilibrium points. Stability analysis shows that the equilibrium point is stable local and global asymptotic if R0 < 1 and unstable if R0 > 1. Then a sensitivity analysis was carried out to determine the parameters that greatly affect the model as well as furthermore, numerical simulations are given to describe the behavior of the model that has been obtained based on the analysis of the sensitivity of basic reproductive numbers, obtained several parameters that affect the spread of COVID-19. Numerical simulation results show that vaccination can suppress the addition of infected populations and depend on the level of effectiveness of vaccination.

Keywords


Dynamic Analysis; Lyapunov function; Sensitivity Analysis; COVID-19; Vaccinate

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References


Kementerian Kesehatan, “Pertanyaan dan Jawaban Terkait COVID-19,” 2020. [Online]. Available: https://infeksiemerging.kemkes.go.id/uncategorized/qna-pertanyaan-dan-jawaban-terkait-covid-19 (Accessed 20 November 2021).

I. Darti, A. Suryanto, H. S. Panigoro, and H. Susanto, “Forecasting COVID-19 Epidemic in Spain and Italy Using A Generalized Richards Model with Quantified Uncertainty,” Communication in Biomathematical Sciences, vol. 3, no. 2, pp. 90–100, 2020. DOI: 10.5614/cbms.2020.3.2.1

D. Aldila, M. Z. Ndii, and B. M. Samiadji, “Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness,” Mathematical Biosciences and Engineering, vol. 17, no. 6, pp. 6355–6389, 2020. DOI: 10.3934/mbe.202033

M. Z. Ndii, Pemodelan Matematika Dinamika Populasi Dan Penyebaran Penyakit Teori, Aplikasi, Dan Numerik. Deepublish, 2018. ISBN 9786232090354.

M. A. Khan and A. Atangana, “Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative,” Alexandria Engineering Journal, vol. 59, no. 4, pp. 2379–2389, 2020. DOI: 10.1016/j.aej.2020.02.033

R. Resmawan, A. R. Nuha, and L. Yahya, “Analisis Dinamik Model Transmisi COVID-19 dengan Melibatkan Intervensi Karantina,” Jambura Journal of Mathematics, vol. 3, no. 1, pp. 66–79, 2021. DOI: 10.34312/jjom.v3i1.8699

S. Annas, M. Isbar Pratama, M. Rifandi, W. Sanusi, and S. Side, “Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia,” Chaos, Solitons and Fractals, vol. 139, p. 110072, 2020. DOI: 10.1016/j.chaos.2020.110072

R. Resmawan and L. Yahya, “Sensitifity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission,” CAUCHY, vol. 6, no. 2, p. 91, 2020. DOI: 10.18860/ca.v6i2.9165

A. A. Gebremeskel, H. W. Berhe, and H. A. Atsbaha, “Mathematical modelling and analysis of COVID-19 epidemic and predicting its future situation in Ethiopia,” Results in Physics, vol. 22, p. 103853, 2021. DOI: 10.1016/j.rinp.2021.103853

R. Resmawan, “Model Epidemik SEIRS-SEI Penyebaran Penyakit Malaria dengan Vaksinasi dan Pengobatan,” in Prosiding Seminar Nasional Matematika IndoMS Wilayah Sulawesi. IndoMS, 2017, pp. 128-140.

J. Giesecke, Modern Infectious Disease Epidemiology, third edit ed. London: CRC Press, 2017. ISBN 9781315222714. DOI: 10.1201/9781315222714

B. Rinaldi, “Pemodelan Matematika Penyebaran Penyakit Corona Viruses Disease 2019 (COVID-19) pada Kasus Penggunaan Masker Kesehatan,” Skripsi, Universitas Jambi, 2021.

M. Azizah, “Model Matematika Penyebaran Penyakit Coronavirus Disease 2019 (COVID-19) Dengan Vaksinasi, Isolasi mandiri, dan Karantina di Rumah Sakit,” Ph.D. dissertation, UIN Syarif Hidayatullah, 2021.

N. Chitnis, J. M. Hyman, and J. M. Cushing, “Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model,” Bulletin of Mathematical Biology, vol. 70, no. 5, pp. 1272–1296, 2008. DOI: 10.1007/s11538-008-9299-0




DOI: https://doi.org/10.34312/jjbm.v3i1.13176

Copyright (c) 2022 Resmawan Resmawan, Lailany Yahya, Revandi S. Pakaya, Hasan S. Panigoro, Agusyarif Rezka Nuha

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