Susceptible Vaccine Infected Removed (SVIR) Model for COVID-19 Cases in Indonesia

Hanna Arini Parhusip, Suryasatriya Trihandaru, Bernadus Aryo Adhi Wicaksono, Denny Indrajaya, Yohanes Sardjono, Om Prakash Vyas


Analysis of data on COVID-19 cases in Indonesia is shown by using the Susceptible Vaccine Infected Removed (SVIR) in this article. In the previous research, cases in the period March-May 2021 were studied, and the reproduction number was computed based on the Susceptible Infected Removed (SIR) model. The prediction did not agree with the real data. Therefore the objective of this article is to improve the model by adding the vaccine variable leading to the new model called the SVIR model as the novelty of this article. The used data are collected from COVID-19 cases of the Indonesian population published by the Indonesian government from March 2020-April 2022. However, the vaccinated persons with COVID-19 cases have been recorded since January 2022. Therefore the models rely on the period January 2021-March 2022, where the parameters in the SIR and SVIR models are determined in this period. The method used is discretizing the models into linear systems, and these systems are solved by Ordinary Least Square (OLS) for time-dependent parameters. It is assumed that the birth rate and death rate in the considered period are constant. Additionally, individuals who have recovered from COVID-19 will not be infected again, and vaccination is not necessarily twice. Furthermore, individuals who have been vaccinated will not be infected with the COVID-19 virus. The SVIR model has captured 3 waves of COVID-19 cases that are appropriate to the real situation in Indonesia from January 2021-March 2022. Additionally, the reproduction numbers as functions of time have been generated. The fluctuations of reproduction numbers agree with the real data. For further research, different regions such as districts in Java and other islands will also be analyzed as the implication of this research.


Bagal, D. K., A. Rath, A. Barua, and D. Patnaik (2020). Estimating the Parameters of Susceptible-Infected Recovered Model of COVID-19 Cases in India During Lockdown Periods. Chaos, Solitons & Fractals, 140; 110154

Britton, T., F. Ball, and P. Trapman (2020). A Mathematical Model Reveals the Influence of Population Heterogeneity on Herd Immunity to SARS-CoV-2. Science, 369(6505); 846–849

Cooper, I., A. Mondal, and C. G. Antonopoulos (2020). A SIR Model Assumption for the Spread of COVID-19 in Different Communities. Chaos, Solitons & Fractals, 139; 110057

Djilali, S. and S. Bentout (2021). Global Dynamics of SVIR Epidemic Model with Distributed Delay and Imperfect Vaccine. Results in Physics, 25; 104245

Emmert-Streib, F. and M. Dehmer (2019). Evaluation of Regression Models: Model Assessment, Model Selection and Generalization Error. Machine Learning and Knowledge Extraction, 1(1); 521–551

Etbaigha, F., A. R. Willms, and Z. Poljak (2018). An SEIR Model of Influenza A Virus Infection and Reinfection within a Darrow-to-Finish Swine Farm. PLOS One, 13(9); e0202493

Fajar, M. and U. Padjadjaran (2020). Estimation of COVID-19 Reproductive Number Case of Indonesia. Badan Pusat Statistik Indonesia

Giesecke, J. (2017). Modern Infectious Disease Epidemiology. CRC Press

Huang, F. L. (2018). Multilevel Modeling and Ordinary Least Squares Regression: How Comparable are They? The Journal of Experimental Education, 86(2); 265–281

Ito, K., C. Piantham, and H. Nishiura (2022). Relative Instantaneous Reproduction Number of Omicron SARS CoV-2 Variant with Respect to the Delta Variant in Denmark. Journal of Medical Virology, 94(5); 2265–2268

Jannah, M., M. A. Karim, and Y. Yulida (2021). Analisis Kestabilan Model Seir untuk Penyebaran Covid-19 dengan Parameter Vaksinasi. BAREKENG Jurnal Ilmu Matematika Dan Terapan, 15(3); 535–542 (in Indonesia)

Jørgensen, S. B., K. Nygård, O. Kacelnik, and K. Telle (2022). Secondary Attack Rates for Omicron and Delta Variants of SARS-CoV-2 in Norwegian Households. Journal of the American Medical Association, 327(16); 1610–1611

Karim, S. S. A. and Q. A. Karim (2021). Omicron SARS-CoV-2 Variant: a New Chapter in the COVID-19 Pandemic. The Lancet, 398(10317); 2126–2128

Koehrsen, W. (2018). Overfitting vs. Underfitting: a Complete Example. Towards Data Science; 1–12

Kretzschmar, M. E., B. Ashby, E. Fearon, C. E. Overton, J. Panovska-Griffiths, L. Pellis, M. Quaife, G. Rozhnova, F. Scarabel, and H. B. Stage (2022). Challenges for Modelling Interventions for Future Pandemics. Epidemics, 38; 100546

Leedy, P. D. and J. E. Ormrod (2019). Practical Research: Planning and Design. ERIC

Overton, C. E., H. B. Stage, S. Ahmad, J. Curran-Sebastian, P. Dark, R. Das, E. Fearon, T. Felton, M. Fyles, and N. Gent (2020). Using Statistics and Mathematical Modelling to Understand Infectious Disease Outbreaks: COVID-19 as an Example. Infectious Disease Modelling, 5; 409–441

Pambuccian, S. E. (2020). The COVID-19 Pandemic: Implications for the Cytology Laboratory. Journal of the American Society of Cytopathology, 9(3); 202–211

Parhusip, H. A. (2020). Menelusuri Covid-19 di Dunia dan di Indonesia dengan Model Regresi SVM, Bayesian dan Gaussian. Jurnal Ilmiah Sains Vol, 20(2); 49–57 (in Indonesia)

Sennott, S. C., J. C. Light, and D. McNaughton (2016). AAC Modeling Intervention Research Review. Research and Practice for Persons with Severe Disabilities, 41(2); 101–115

Sifriyani, S., U. Mulawarman, and D. Rosadi (2020). Pemodelan Susceptible Infected Recovered (Sir) untuk Estimasi Angka Reproduksi Covid-19 di Kalimantan Timur dan Samarinda. Jurnal Media Statistika, July; 1–13 (in Indonesia)

Simon, M. (2011). Assumptions, Limitations and Delimitations. Dissertation and Scholarly Research: Recipes for Success

Sundnes, J. (2020). Solving Ordinary Differential Equations in Python. Simula Research Laboratory and Department of Informatics, University of Oslo

Trihandaru, S., H. A. Parhusip, B. Susanto, and Y. Sardjono (2021). Simple Forward Finite Dierence for Computing Reproduction Number of COVID-19 in Indonesia During the New Normal. JTAM (Jurnal Teori dan Aplikasi Matematika), 5(1); 88–99

Witbooi, P. J., G. E. Muller, and G. J. Van Schalkwyk (2015). Vaccination Control in a Stochastic SVIR Epidemic Model. Computational and Mathematical Methods in Medicine, 2015

World Health Organization (2022). Statement – Update on COVID-19: Omicron Wave Threatening to Overcome Health Workforce. World Health Organization


Hanna Arini Parhusip (Primary Contact)
Suryasatriya Trihandaru
Bernadus Aryo Adhi Wicaksono
Denny Indrajaya
Yohanes Sardjono
Om Prakash Vyas
Parhusip, H. A., Trihandaru, S., Wicaksono, B. A. A. ., Indrajaya, D. ., Sardjono, Y. ., & Vyas, O. P. (2022). Susceptible Vaccine Infected Removed (SVIR) Model for COVID-19 Cases in Indonesia. Science and Technology Indonesia, 7(3), 400–408.

Article Details