Systematic Literature Review Model Matematika Kompartemen pada Penyakit dan Kontagion Sosial
Keywords:
epidemic-type model, SIR, SEIR, SEIRS, social contagion
Abstract
Epidemic-type mathematical compartmental models are no longer limited to biological infectious diseases; they are increasingly adapted to behavioral and social contagion phenomena. This study aimed to systematically review the use of SIR, SEIR, SEIRS, and modified compartmental models in infectious disease transmission and social phenomena. A systematic literature review was conducted by screening 24 full-text articles collected from journal databases and publisher repositories from 2020 to 2026. Eighteen primary modelling studies were included in the main synthesis, while six review or guideline articles were used as theoretical and methodological support. Data were extracted on model type, domain, compartments, data source, mathematical analysis, simulation method, software, and major findings. The reviewed infectious disease studies addressed tuberculosis, malaria, COVID-19, and typhus, whereas social-domain studies covered online game addiction, social media addiction (TikTok), online gambling, gambling crime, and impulsive buying. SEIR was the most frequent structure, followed by SEIRS and SIR. Most studies calculated equilibrium points and the basic reproduction number; fewer studies reported sensitivity analysis, parameter calibration, uncertainty analysis, or empirical validation. The findings indicate that compartmental models are flexible analytical tools across biological and social systems, but future studies need stronger reporting transparency, parameter justification, validation, and reproducible simulation procedures.
References
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Anwar, A., Syam, R., Pratama, M. I., & Side, S. (2021). SEIRS model analysis for online game addiction problem of mathematics students. Journal of Physics: Conference Series, 1918, 042024. https://doi.org/10.1088/1742-6596/1918/4/042024
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Chaturvedi, M., Bartz, A., Denkinger, C. M., Klett-Tammen, C., Kretzschmar, M., Kuhlmann, A., Lange, B., Marx, F. M., Mikolajczyk, R., Monsef, I., Nguyen, H. T., Suer, J., Skoetz, N., Jaeger, V. K., & Karch, A. (2026). Guidelines on reporting and assessing dynamic mathematical models of infectious diseases: A scoping review. BMC Infectious Diseases, 26, 182. https://doi.org/10.1186/s12879-025-12211-8
Cuesta-Herrera, L., Pastenes, L., Cordova-Lepe, F., Arencibia, A. D., Torres-Mantilla, H., & Gutierrez-Jara, J. P. (2022). Analysis of SEIR-type models used at the beginning of COVID-19 pandemic reported in high-impact journals. Medwave, 22(8), e2552. https://doi.org/10.5867/medwave.2022.08.2552
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Inayah, N., Manaqib, M., Fitriyati, N., & Yupinto, I. (2020). Model matematika penyebaran penyakit pulmonary tuberculosis dengan penggunaan masker medis. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 14(3), 459-470. https://doi.org/10.30598/barekengvol14iss3pp459-570
Irwan, Pathuddin, H., & Ahmad, N. R. A. (2023). Analisis model SEIR (Susceptible, Exposed, Infected, Recovered) pada penyebaran penyakit tifus di Kota Makassar. ELIPS: Jurnal Pendidikan Matematika, 4(1), 58-69.
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Ramadhan, N. R., & Kalla, N. R. (2025). Perilaku impulsive buying model SEIR pada mahasiswa saat flash sale TikTok. VENN: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences, 5(3). https://doi.org/10.53696/venn.v5i3.470
Rangkuti, Y. M., Firmansyah, & Landong, A. (2022). Sensitivity analysis of SEIR epidemic model of Covid 19 spread in Indonesia. Journal of Physics: Conference Series, 2193, 012092. https://doi.org/10.1088/1742-6596/2193/1/012092
Robby, R. R. (2025). Analisis kestabilan model SEIR pada penyebaran penyakit malaria dengan 2 tingkat penyebaran infeksi yang berbeda. Journal of Innovative and Creativity, 5(2), 21359-21367.
Side, S., Muzakir, N. A., Pebriani, D., & Utari, S. N. (2020). Model SEIR kecanduan game online pada siswa di SMP Negeri 3 Makassar. Jurnal Sainsmat, 9(1), 91-102.
Siregar, A. F. P., Firmansyah, & Panjaitan, D. J. (2024). Pemodelan matematika terhadap kecanduan game online berdasarkan model SEIRS pada berbagai kelompok usia di Indonesia. Majalah Ilmiah Methoda, 14(1), 87-92. https://doi.org/10.46880/methoda.Vol14No1.pp87-92
Situmeang, H. S., & Syahputra, M. R. (2024). Model SEIRS terhadap kejahatan perjudian di kalangan masyarakat (Studi kasus: Pengadilan Negeri Batam). MES: Journal of Mathematics Education and Science, 10(1), 140-150.
Sweileh, W. M. (2022). Global research activity on mathematical modeling of transmission and control of 23 selected infectious disease outbreak. Globalization and Health, 18, 4. https://doi.org/10.1186/s12992-022-00803-x
Syahfitri, F. I., Siahaan, E. H. B., Ningsih, F. I., & Sitompul, A. (2025). Model matematika terhadap dinamika kecanduan judi online pada masyarakat Desa Tanjung Putus. Jurnal Arjuna: Publikasi Ilmu Pendidikan, Bahasa dan Matematika, 3(1), 323-330. https://doi.org/10.61132/arjuna.v3i1.1607
Syam, R., Side, S., & Said, C. S. (2020). Model SEIRS penyebaran penyakit tuberkulosis di Kota Makassar. Journal of Mathematics, Computations, and Statistics, 3(1), 11-19.
Tang, L., Zhou, Y., Wang, L., Purkayastha, S., Zhang, L., He, J., Wang, F., & Song, P. X. K. (2020). A review of multi-compartment infectious disease models. International Statistical Review, 88(2), 462-513. https://doi.org/10.1111/insr.12402
Aguiar, M., Anam, V., Blyuss, K. B., Estadilla, C. D. S., Guerrero, B. V., Knopoff, D., Kooi, B. W., Srivastav, A. K., Steindorf, V., & Stollenwerk, N. (2022). Mathematical models for dengue fever epidemiology: A 10-year systematic review. Physics of Life Reviews, 40, 65-92. https://doi.org/10.1016/j.plrev.2022.02.001
Anwar, A., Syam, R., Pratama, M. I., & Side, S. (2021). SEIRS model analysis for online game addiction problem of mathematics students. Journal of Physics: Conference Series, 1918, 042024. https://doi.org/10.1088/1742-6596/1918/4/042024
Aziz, A., Azzahra, L., Sari, S. L., Zaman, A. M., & Rumite, W. (2024). Model matematika kecanduan media sosial Tiktok pada siswa: Sebuah kajian dengan pendekatan SEI1I2I3R. Mandalika Mathematics and Education Journal, 6(2), 608-623. https://doi.org/10.29303/jm.v6i2.7129
Bahari, M. F., Lillah, S. S., Zahro, A., & Sari, M. P. (2023). Model SIR untuk penyebaran tuberkulosis di Kabupaten Jepara. Jurnal Ilmu Komputer dan Matematika, 4(2), 37-43.
Chaturvedi, M., Bartz, A., Denkinger, C. M., Klett-Tammen, C., Kretzschmar, M., Kuhlmann, A., Lange, B., Marx, F. M., Mikolajczyk, R., Monsef, I., Nguyen, H. T., Suer, J., Skoetz, N., Jaeger, V. K., & Karch, A. (2026). Guidelines on reporting and assessing dynamic mathematical models of infectious diseases: A scoping review. BMC Infectious Diseases, 26, 182. https://doi.org/10.1186/s12879-025-12211-8
Cuesta-Herrera, L., Pastenes, L., Cordova-Lepe, F., Arencibia, A. D., Torres-Mantilla, H., & Gutierrez-Jara, J. P. (2022). Analysis of SEIR-type models used at the beginning of COVID-19 pandemic reported in high-impact journals. Medwave, 22(8), e2552. https://doi.org/10.5867/medwave.2022.08.2552
Eegunjobi, A. S., & Makinde, O. D. (2022). Mathematical analysis of two strains Covid-19 disease using SEIR model. Journal of Mathematical and Fundamental Sciences, 54(2), 211-232. https://doi.org/10.5614/j.math.fund.sci.2022.54.2.1
Herzog, S. A., Blaizot, S., & Hens, N. (2017). Mathematical models used to inform study design or surveillance systems in infectious diseases: A systematic review. BMC Infectious Diseases, 17, 775. https://doi.org/10.1186/s12879-017-2874-y
Indah, A. P., & Maulana, D. A. (2022). Model dinamika kecanduan media sosial: Studi kasus kecanduan TikTok pada mahasiswa FMIPA UNESA. MATHunesa: Jurnal Ilmiah Matematika, 10(1), 131-139.
Inayah, N., Manaqib, M., Fitriyati, N., & Yupinto, I. (2020). Model matematika penyebaran penyakit pulmonary tuberculosis dengan penggunaan masker medis. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 14(3), 459-470. https://doi.org/10.30598/barekengvol14iss3pp459-570
Irwan, Pathuddin, H., & Ahmad, N. R. A. (2023). Analisis model SEIR (Susceptible, Exposed, Infected, Recovered) pada penyebaran penyakit tifus di Kota Makassar. ELIPS: Jurnal Pendidikan Matematika, 4(1), 58-69.
Kermack, W. O., & McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society A, 115(772), 700-721. https://doi.org/10.1098/rspa.1927.0118
Lestari, N. D., Arimanda, A. R. Y., & Nisa, G. A. (2025). Simulasi SIR kecanduan media sosial mahasiswa FMIPA UNRAM dengan metode Euler dan Heun. JSN: Jurnal Sains Natural, 3(2), 96-106. https://doi.org/10.35746/jsn.v3i2.716
Mohajan, D., & Mohajan, H. K. (2023). Mathematical analysis of SEIR model to prevent COVID-19 pandemic. Munich Personal RePEc Archive Paper No. 115858.
Page, M. J., McKenzie, J. E., Bossuyt, P. M., Boutron, I., Hoffmann, T. C., Mulrow, C. D., Shamseer, L., Tetzlaff, J. M., Akl, E. A., Brennan, S. E., Chou, R., Glanville, J., Grimshaw, J. M., Hrobjartsson, A., Lalu, M. M., Li, T., Loder, E. W., Mayo-Wilson, E., McDonald, S., ... Moher, D. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372, n71. https://doi.org/10.1136/bmj.n71
Ramadhan, N. R., & Kalla, N. R. (2025). Perilaku impulsive buying model SEIR pada mahasiswa saat flash sale TikTok. VENN: Journal of Sustainable Innovation on Education, Mathematics and Natural Sciences, 5(3). https://doi.org/10.53696/venn.v5i3.470
Rangkuti, Y. M., Firmansyah, & Landong, A. (2022). Sensitivity analysis of SEIR epidemic model of Covid 19 spread in Indonesia. Journal of Physics: Conference Series, 2193, 012092. https://doi.org/10.1088/1742-6596/2193/1/012092
Robby, R. R. (2025). Analisis kestabilan model SEIR pada penyebaran penyakit malaria dengan 2 tingkat penyebaran infeksi yang berbeda. Journal of Innovative and Creativity, 5(2), 21359-21367.
Side, S., Muzakir, N. A., Pebriani, D., & Utari, S. N. (2020). Model SEIR kecanduan game online pada siswa di SMP Negeri 3 Makassar. Jurnal Sainsmat, 9(1), 91-102.
Siregar, A. F. P., Firmansyah, & Panjaitan, D. J. (2024). Pemodelan matematika terhadap kecanduan game online berdasarkan model SEIRS pada berbagai kelompok usia di Indonesia. Majalah Ilmiah Methoda, 14(1), 87-92. https://doi.org/10.46880/methoda.Vol14No1.pp87-92
Situmeang, H. S., & Syahputra, M. R. (2024). Model SEIRS terhadap kejahatan perjudian di kalangan masyarakat (Studi kasus: Pengadilan Negeri Batam). MES: Journal of Mathematics Education and Science, 10(1), 140-150.
Sweileh, W. M. (2022). Global research activity on mathematical modeling of transmission and control of 23 selected infectious disease outbreak. Globalization and Health, 18, 4. https://doi.org/10.1186/s12992-022-00803-x
Syahfitri, F. I., Siahaan, E. H. B., Ningsih, F. I., & Sitompul, A. (2025). Model matematika terhadap dinamika kecanduan judi online pada masyarakat Desa Tanjung Putus. Jurnal Arjuna: Publikasi Ilmu Pendidikan, Bahasa dan Matematika, 3(1), 323-330. https://doi.org/10.61132/arjuna.v3i1.1607
Syam, R., Side, S., & Said, C. S. (2020). Model SEIRS penyebaran penyakit tuberkulosis di Kota Makassar. Journal of Mathematics, Computations, and Statistics, 3(1), 11-19.
Tang, L., Zhou, Y., Wang, L., Purkayastha, S., Zhang, L., He, J., Wang, F., & Song, P. X. K. (2020). A review of multi-compartment infectious disease models. International Statistical Review, 88(2), 462-513. https://doi.org/10.1111/insr.12402
