# THE DEVELOPMENT OF COVID-19 USING OUTBREAK THE SUSCEPTIBLE, INFECTED, AND RECOVERED (SIR) MODEL WITH VACCINATION

• Dorrah Azis Mathematics Department, Faculty of Mathematic and Natural Sciences, University of Lampung, Indonesia
• La Zakaria Mathematics Department, Faculty of Mathematic and Natural Sciences, University of Lampung, Indonesia
• Tiryono Ruby Mathematics Department, Faculty of Mathematic and Natural Sciences, University of Lampung, Indonesia
• Muhammad Is’ad Arifaldi Mathematics Department, Faculty of Mathematic and Natural Sciences, University of Lampung, Indonesia
Keywords: SIR Model, Covid-19, Basic Reproduction Number, Routh-Hurwitz Criterion

### Abstract

The Covid-19 pandemic in 2020 has caused severe problems in Indonesia. The Covid-19 virus epidemic can be modeled using the Susceptible, Infected, and Recovered (SIR) model. This modeling aims to look at the dynamics of Covid-19 to predict when disease-free and endemic disease occurs and to find the basic reproduction number ( ) for policy making in suppressing the spread of Covid-19. In this article, we describe and solve a research result on the SIR model with an assumption. The assumption in the model is that there is vaccination for the population. There are live stages of research conducted. The first is creating the SIR model and determining the equilibrium points on disease-free and disease-endemic. The Second is getting the basic reproduction number. The third is determining the stability around the equilibrium points using the Routh-Hurwitz criteria. Fourth, create a diagram for the subpopulations state at a specific time using Wolfram Mathematica software. As an implementation of the model created, COVID-19 data at the Batanghari Community Health Center Inpatient UPTD was used. Finally, determine the model error percentage with MAPE. The SIR Covid-19 model was made using eight parameters, namely , which are all positive. The results showed that the disease-free and disease-endemic equilibrium points were locally asymptotically stable after being analyzed using the Routh-Hurwitz stability criteria. The model trial using data from UPTD Puskesmas Batanghari obtained a stable condition for up to 100 months with a MAPE of 2.8%. From this study, obtained an . This means that if you want to reduce the rate of spread, then reduce the number of people who are easily infected ( ) and reduce contacts ( ), and increase the healing rate ( ).

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Published
2023-09-30
How to Cite
[1]
D. Azis, L. Zakaria, T. Ruby, and M. Arifaldi, “THE DEVELOPMENT OF COVID-19 USING OUTBREAK THE SUSCEPTIBLE, INFECTED, AND RECOVERED (SIR) MODEL WITH VACCINATION”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1325-1340, Sep. 2023.
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