A SIAR Model Approach to the Impact of Mudik Tradition on Covid-19 Transmission in Indonesia
DOI:
https://doi.org/10.70609/g-tech.v9i3.7308Keywords:
Mathematics modelling, SIAR, Covid-19, mudik traditionAbstract
In Indonesia, on March 2, 2020, the government announced the first case of Covid-19. Preventing the COVID-19 spread in Indonesia is challenging because the people are very diverse, and not everyone has the same understanding of the transmission of COVID-19. In addition, the Indonesians has mudik tradition, going home yearly on Eid al-Fitr. This study developed an epidemic model of Covid-19 spread SIAR by adding migration factors to represent the mudik tradition. The disease-free equilibrium point, the endemic equilibrium point, and its stability were determined. Numerical simulations were done using Covid-19 transmission data to analyze the trend of symptomatic and asymptomatic infected subpopulations. The results show that the dynamic characteristics of Covid-19 cases were semi-stable in compartments S, I, and A. This condition means that S, I, and A will rise at a certain time. In a disease-free situation, the susceptible subpopulation S is stable at a certain value. At the same time, other subpopulations are stable at almost zero and at zero. The susceptible subpopulation S in a disease-free situation is larger than during an epidemic. The number of people in disease-free conditions is smaller than those in epidemic conditions. In addition, migration at a certain level can increase the spread of Covid-19.
References
BPS. (2022). Rata-Rata Laju Pertumbuhan Penduduk Menurut Provinsi (Average Population Growth Rate by Province). https://www.bps.go.id/statictable/2009/02/20/1268/rata-rata-laju-pertumbuhan-penduduk-menurut-provinsi-1971---2022.html
Chen, M., Li, M., Hao, Y., Liu, Z., Hu, L., & Wang, L. (2020). The introduction of population migration to SEIAR for COVID-19 epidemic modeling with an efficient intervention strategy. Information Fusion, 64, 252–258. https://doi.org/10.1016/j.inffus.2020.08.002
Cucinotta, D., & Vanelli, M. (2020). WHO Declares COVID-19 A Pandemic. In Acta Biomedica (Vol. 91, Issue 1, pp. 157–160). Mattioli 1885. https://doi.org/10.23750/abm.v91i1.9397
Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The Construction of Next-Generation Matrices for Compartmental Epidemic Models. Journal of the Royal Society Interface, 7(47), 873–885. https://doi.org/10.1098/rsif.2009.0386
Drucker, D. S. (1979). A Second Look at Descartes’ Rule of Signs. Mathematics Magazine, 52(4), 237–238. https://doi.org/10.1080/0025570X.1979.11976790
Fauzia, L. A. (2021). Analisis Pemodelan Matematika Penularan Covid-19 dengan Tindakan Rawat Inap di Rumah Sakit (Mathematical Modeling Analysis of Covid-19 Transmission with Hospitalization Actions). MATHunesa: Jurnal Ilmiah Matematika, 9(1), 126–132. https://doi.org/10.26740/mathunesa.v9n1.p126-132
Fosu, G. O., Akweittey, E., & Adu-Sackey, A. (2020). Next-Generation Matrices and Basic Reproductive Numbers for All Phases of The Coronavirus Disease. Open Journal of Mathematical Sciences, 4(1), 261–272. https://doi.org/10.30538/oms2020.0117
Gao, Z., Xu, Y., Sun, C., Wang, X., Guo, Y., Qiu, S., & Ma, K. (2021). A Systematic Review of Asymptomatic Infections with Covid-19. Journal of Microbiology, Immunology and Infection, 54(1), 12–16. https://doi.org/10.1016/j.jmii.2020.05.001
Gumel, A. B., Iboi, E. A., Ngonghala, C. N., & Elbasha, E. H. (2021). A Primer on Using Mathematics to Understand COVID-19 Dynamics: Modeling, Analysis and Simulations. Infectious Disease Modelling, 6, 148–168. https://doi.org/10.1016/j.idm.2020.11.005
Hasan, A., Nasution, Y., Susanto, H., Putri, E., Tjahjono, V., Puspita, D., Sukandar, K., Nuraini, N., & Widyastuti, W. (2022). Modeling COVID-19 Transmissions and Evaluation of Large Scale Social Restriction in Jakarta, Indonesia. Communication in Biomathematical Sciences, 5(1), 90–100. https://doi.org/10.5614/cbms.2022.5.1.6
Hu, Z., Wu, Y., Su, M., Xie, L., Zhang, A., Lin, X., & Nie, Y. (2021). Population Migration, Spread of COVID-19, and Epidemic Prevention and Control: Empirical Evidence from China. BMC Public Health, 21(259), 1–12. https://doi.org/10.1186/s12889-021-10605-2
Intan, G. (2021, June 17). Satgas: Kenaikan Kasus COVID-19 Pasca Lebaran 2021 Lebih Tinggi dari Tahun Lalu. VOA Indonesia. https://www.voaindonesia.com/a/satgas-kenaikan-kasus-covid-19-pasca-lebaran-2021-lebih-tinggi-dari-tahun-lalu/5932653.html
Joyosemito, I. S., & Nasir, N. M. (2021). Pendekatan Pemodelan Matematika Dinamis Dalam Analisis Prediksi COVID-19 Sebagai Masukan Kebijakan Pemerintah Indonesia (Dynamic Mathematical Modeling Approach in COVID-19 Prediction Analysis as Policy Input for the Indonesian Government). Jurnal Pengabdian Kepada Masyarakat UBJ, 4(1), 1–16. https://doi.org/10.31599/jabdimas.v4i1.455
Kasbawati. (2009). Penentuan Nilai R0 dengan Menggunakan Operator The Next Generation (Determining the R0 Value Using the Next Generation Operator). Jurnal Matematika, Statistika, Dan Komputasi, 6(1), 59–64. https://doi.org/https://doi.org/10.20956/jmsk.v7i1.3373
Khrapov, P. V., & Loginova, A. A. (2020). Mathematical Modelling of the Dynamics of the Coronavirus COVID-19 Epidemic Development in China. International Journal of Open Information Technologies, 8(4), 13–16.
Kontan, R. (2025, March 20). Jumlah Pemudik 2016-2025. Kementerian Perhubungan. https://pusatdata.kontan.co.id/infografik/83/Jumlah-Pemudik-2016-2025
Nag, S. (2020). A Mathematical Model in The Time of Covid-19. https://doi.org/10.31219/osf.io/8n92h
Olivia, S., Gibson, J., & Nasrudin, R. (2020). Indonesia in The Time of Covid-19. Bulletin of Indonesian Economic Studies, 56(2), 143–174. https://doi.org/10.1080/00074918.2020.1798581
Panovska-Griffiths, J. (2020). Can Mathematical Modelling Solve the Current Covid-19 Crisis? BMC Public Health, 20(1). https://doi.org/10.1186/s12889-020-08671-z
Sekretariat. (2022). 273 Juta Penduduk Indonesia Terupdate Versi Kemendagri (273 Million Indonesian Population Updated Version of Ministry of Home Affairs). Kementerian Dalam Negeri Republik Indonesia. https://dukcapil.kemendagri.go.id/phln/read/273-juta-penduduk-indonesia-terupdate-versi-kemendagri
Setiati, S., & Azwar, M. K. (2020). COVID-19 and Indonesia. Acta Medica Indonesiana, 52(1), 84–89. https://doi.org/10.1111/tmi.13383
Thompson, I. (2017). Understanding Maple. Cambridge University Press.
Velavan, T. P., & Meyer, C. G. (2020). The COVID-19 Epidemic. Tropical Medicine and International Health, 25(3), 278–280. https://doi.org/10.1111/tmi.13383
Winardi, W., Karyono, Y., Nugroho, A., Adi, W. P., Budiati, I., Riyadi, Lestari, T. H., Mardiana, Lasma, Sorayan, P. H., & Suswandi. (2022). Statistical Yearbook of Indonesia 2022. BPS. https://www.bps.go.id/id/publication/2022/02/25/0a2afea4fab72a5d052cb315/statistik-indonesia-2022.html
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Darsih Idayani, Asmara Iriani Tarigan, Selly Anastassia Amellia Kharis, Heny Kurniawati
This work is licensed under a Creative Commons Attribution 4.0 International License.
