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

Abstract

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.

Keywords

• covid-19
• sir
• svir
• vaccination
• reproduction number