Analisis Stabilitas Model Penyebaran Penyakit Menular Dengan Vaksinasi di Indonesia

Authors

  • Ivan Adhi Prasetyantono Universitas Nusa Mandiri
  • Aditama Surya Permana Universitas Nusa Mandiri
  • Odiyanto Cahyo Kusumo Universitas Nusa Mandiri

Keywords:

Infectious diseases, SIRV model, Vaccination, stability, Population dynamics. A.

Abstract

Infectious diseases are one of the major health problems in Indonesia. Mathematical models can help understand the dynamics of disease spread and the impact of vaccination programs. This study uses the SIRV (Susceptible-Infected-Recovered-Vaccinated) model to analyze the stability of disease spread and the impact of vaccination on the population. This study was conducted through fixed-point equilibrium analysis and numerical simulations to assess the effectiveness of vaccination in reducing transmission rates. The results showed that vaccination has a significant role in controlling the spread of the disease.

References

Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: Dynamics and control. Oxford University Press.

Diekmann, O., Heesterbeek, J. A. P., & Britton, T. (2012). Mathematical tools for understanding infectious disease dynamics. Princeton University Press.

Ferguson, N. M., et al. (2006). Strategies for mitigating an influenza pandemic. Nature, 442(7101), 448-452. https://doi.org/10.1038/nature05005

Ghosh, M., & Roy, P. (2016). Modeling of disease transmission and stability analysis with vaccination. Computational and Mathematical Methods in Medicine, 2016, Article ID 9570531. https://doi.org/10.1155/2016/9570531

Gray, A., Greenhalgh, D., Hu, L., Mao, X., & Pan, J. (2011). A stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics, 71(3), 876-902. https://doi.org/10.1137/10079292X

Katul, G. G., Simon, K. R., & Zhang, S. (2020). Linking COVID-19 with weather patterns and stability in Indonesia. Journal of Infectious Disease Dynamics, 48(2), 190-201. https://doi.org/10.1016/j.jid.2020.02.010

Li, J., & Cui, J. (2004). The spread of infectious diseases in populations with varying vaccine coverage. Mathematical Biosciences, 192(2), 217-232. https://doi.org/10.1016/j.mbs.2004.03.004

Rahman, A., & Siregar, S. A. (2022). Dampak program vaksinasi COVID-19 terhadap penyebaran di Indonesia: Sebuah model SIR. Jurnal Matematika dan Sains Terapan, 18(4), 217-227.

Rahman, M., & Islam, S. (2018). Impact of vaccination on the dynamics of infectious disease spread: A SIR model analysis. Journal of Applied Mathematics, 2018, Article ID 3827417. https://doi.org/10.1155/2018/3827417

Samanta, G. P., & Saha, S. (2010). Analysis of stability of a vaccinated SIR model. Mathematical and Computer Modelling, 52(5-6), 839-849. https://doi.org/10.1016/j.mcm.2010.03.019

Sari, A. M., & Wahyuni, R. (2021). Pemodelan penyebaran COVID-19 di Indonesia dengan faktor vaksinasi menggunakan pendekatan SEIR. Jurnal Epidemiologi Indonesia, 12(3), 332-345.

Wang, W., & Zhao, X. Q. (2017). Threshold dynamics for compartmental epidemic models in periodic environments. Journal of Dynamics and Differential Equations, 29(4), 1361-1383. https://doi.org/10.1007/s10884-017-9652-z

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Published

2025-01-31

Issue

Vol. 1 No. 1 (2025): Prosiding Seminar Nasional Ilmu Matematika dan Sains

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Articles

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