A comparison of models that can be used in case estimations in epidemics: Estimating the number of COVID-19 cases

In order to control the epidemic, which may have serious effects on society in terms of health, economy and education, it is necessary to determine the causes of the disease, prevent transmission and treat patients quickly. In the course of implementing these steps, it is of great importance to monitor the disease's progression and the number of cases. Consequently, mathematical models that can estimate the number of new cases have always been needed. These models, which became popular in the early 20th century, vary in terms of their predictive success. In this thesis, the SIR model and the ARIMA model, which are frequently used among these models, were compared using Covid-19 pandemic data and their advantages and disadvantages were determined. In this thesis, 550-day data were used, starting from the day the first case was seen in Germany, America, Turkey and the Czech Republic. In order to estimate the parameters of the SIR model, previous 3, 5 and 7-day values were employed. The daily case numbers and as well as the weekly total case numbers were estimated using the models. The frequency value in the ARIMA model was set at 365 and 52. The performance of the models were examined using root mean square error (RMSE) values and trend graphs. The results of the analyses indicated that the number of days to be used for parameter estimation in the SIR model affected the performance of the SIR model. Furthermore, the use of 5 or 7 days generally increased the estimation success. Additionally, it was observed that the ARIMA model has lower RMSE values in daily case estimations than in weekly case estimations. The findings of this study indicate that the models do not exhibit a significant degree of superiority over one another. Furthermore, the study revealed that at least five days of data are required for parameter estimation in the SIR model, while longer data periods are necessary for weekly case estimation in ARIMA models.