Stochastic SEIR Model for Simulating Epidemic Dynamics in Limited Populations
DOI:
https://doi.org/10.62951/switch.v3i1.333Keywords:
Epidemic, SEIR, Epidemiology, PopulationAbstract
The stochastic SEIR model offers an innovative approach to understanding the spread of infectious diseases, particularly tuberculosis, in limited populations. This study adopts a stochastic model to capture random variability in individual interactions, often overlooked in deterministic models. The population is divided into four main categories: Susceptible (S), Exposed (E), Infected (I), and Recovered (R), with transitions between categories determined by probabilities based on epidemiological parameters. Through simulations, the model demonstrates its capability to depict more realistic patterns of disease spread, including fluctuations in case numbers and epidemic duration. The findings indicate that stochastic variability plays a crucial role in understanding the dynamics of tuberculosis transmission, especially in small populations or when the number of individual contacts is limited. The stochastic SEIR model can serve as an effective tool for policymakers to evaluate various intervention strategies, such as vaccination, transmission control, and treatment, as well as to design public health policies that are data-driven and adaptive to epidemiological uncertainties.
Downloads
References
Afriansyah, D., Dilla, H., Sumarno, H., & Mangku, I. W. (2023). Model stokastik epidemik SIRS insiden tak linear dengan vaksinasi. MILANG Journal of Mathematics and Its Applications, 19(1), 11–22. https://doi.org/10.29244/milang.19.1.11-22
Aidid, M. A., Kasim, M., & Tiro, M. (2020). Analisis model epidemi stokastik SEIR pada penyakit tuberculosis di Kota Makassar dengan ABSEIR. Prosiding Seminar Nasional Venue Artikulasi-Riset, Inovasi, Resonansi-Teori, dan Aplikasi Statistika (VARIANSI), 2(2), 160–170.
Anderson, R. M. (1991). Infectious diseases of humans: Dynamics and control. Oxford University Press.
Aziezah, N., Sumarno, H., & Jaharuddin, J. (2024). Model stokastik pada penyebaran penyakit tuberkulosis. Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika, 11(2), 72–80. https://doi.org/10.31316/jderivat.v10i2.5573
Bellomo, N., Burini, D., & Outada, N. (2022). Multiscale models of COVID-19 with mutations and variants. Networks and Heterogeneous Media, 17(3), 293–310. https://doi.org/10.3934/nhm.2022008
Brauer, F., Van den Driessche, P., & Wu, J. (2008). Mathematical epidemiology (Vol. 1).
Cocomello, J., & Ramanan, K. (2023). Exact description of limiting SIR and SEIR dynamics on locally tree-like graphs. Unpublished manuscript, 1–45.
Engbert, R., Rabe, M. M., Kliegl, R., & Reich, S. (2021). Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics. Bulletin of Mathematical Biology, 83(1), 1–16. https://doi.org/10.1007/s11538-020-00834-8
Greenhalgh, T. (2021). Miasmas, mental models and preventive public health: Some philosophical reflections on science in the COVID-19 pandemic. Interface Focus, 11(6). https://doi.org/10.1098/rsfs.2021.0017
Guan, J., Wei, Y., Zhao, Y., & Chen, F. (2020). Modeling the transmission dynamics of COVID-19 epidemic: A systematic review. Journal of Biomedical Research, 34(6), 422–430. https://doi.org/10.7555/JBR.34.20200119
Halloran, M. E., Longini, I. M., & Struchiner, C. J. (2010). Binomial and stochastic transmission models. In Design and analysis of vaccine studies (pp. 63–84).
Hassan, M. H., El-Azab, T., Alnemer, G., & Sohaly, M. A. (2024). Analysis time-delayed SEIR model with survival rate for COVID-19 stability and disease control. Unpublished manuscript, 1–16.
Hernández, P., Pena, C., Ramos, A., & Gómez-Cadenas, J. J. (2020). A simple formulation of non-Markovian SEIR. Unpublished manuscript, 1–21.
Khaerunnisa, N. A., Nasution, Y. N., & Huda, M. N. (2022). Analisis kestabilan model epidemik SEI pada penyebaran penyakit tuberkulosis. BASIS Jurnal Ilmiah Matematika, 1(1), 16–29.
Lee, G., Choi, W., Jo, H., Park, W., & Kim, J. (2020). Analysis of motor control strategy for frontal and sagittal planes of circular tracking movements using visual feedback noise from velocity change and depth information. PLoS ONE, 15(11), 1–22. https://doi.org/10.1371/journal.pone.0241138
Nisa, K., Rahman, H., & Kusumastuti, A. (2022). Model epidemi suspected exposed infected recovered (SEIR) pada penyebaran COVID-19 orde-fraksional. Jurnal Riset Mahasiswa Matematika, 1(3), 156–164. https://doi.org/10.18860/jrmm.v1i3.14440
Ríos-Gutiérrez, A., Torres, S., & Arunachalam, V. (2023). An updated estimation approach for SEIR models with stochastic perturbations: Application to COVID-19 data in Bogotá. PLoS ONE, 18(8), 1–30. https://doi.org/10.1371/journal.pone.0285624
Rohimasanti, W., Respatiwulan, & Pratiwi, H. (2021). Model epidemi stokastik SIR rantai binomial. Seminar Nasional Official Statistics, 2020(1), 1239–1246. https://doi.org/10.34123/semnasoffstat.v2020i1.674
Siettos, C. I., & Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Virulence, 4(4), 295–306.
Taghizadeh, E., & Mohammad-Djafari, A. (2022). SEIR modeling, simulation, parameter estimation, and their application for COVID-19 epidemic prediction. Physical Sciences Forum, 18. https://doi.org/10.3390/psf2022005018
Wicaksono, D., Respatiwulan, & Susanti, Y. (2019). Model discrete time Markov chain (DTMC) susceptible infected recovered (SIR) pada pola penyebaran penyakit cacar air. Prosiding Seminar Nasional Sains & Entrepreneurship VI, 1(1), 1–8.
Zhang, Z., Zeb, A., Hussain, S., & Alzahrani, E. (2020). Dynamics of COVID-19 mathematical model with stochastic perturbation. Advances in Difference Equations, 2020(1), 1–12. https://doi.org/10.1186/s13662-020-02909-1
Zhao, Y., Wang, H., & Wang, D. (2024). The dynamic behavior of a stochastic SEIRM model of COVID-19 with standard incidence rate. Mathematics, 12(19). https://doi.org/10.3390/math12192966
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Switch : Jurnal Sains dan Teknologi Informasi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
