As a case study for our research, COVID-19, that was caused by a unique coronavirus, has substantially affected the globe, not only in terms of healthcare, but also in terms of economics, education, transportation, and politics. Predicting the pandemic's course is critical to combating and tracking its spread. The objective of our study is to evaluate, optimize and fine-tune state of the art prediction models in order to enhance its performance and to automate its function as possible. Therefore, a comparison between statistical versus compartmental methods for time series-based modeling and forecasting of infectious disease progression was conducted. The comparison included several classical univariate time series statistical models, including Exponential Smoothing, Holt, Holt-Winters, and Seasonal Auto Regressive Integrated Moving Average (SARIMA), as opposed to an optimized version of the compartmental multivariate epidemiological model SEIRD, which is referred to in our study, as, Non-Linear L-BFGS-B Fitted SEIRD. The mentioned methods were implemented and fine-tuned to model and forecast COVID-19 outbreak situation represented by confirmed cases, recoveries, and fatalities in (Australia, Canada, Egypt, India, United States of America and United Kingdom). Through the implementing and tuning of both types of models, we have observed that while univariate time series forecasting models such as SARIMA produce highly accurate predictions due to their ease of use and procedure, as well as their ability to deal with seasonality and cycles in time series, multivariate epidemiological models are more powerful and extendible. Despite their complexity, epidemiological models have aided extensively in understanding the spread and severity of infectious disease pandemics such as the COVID-19 global pandemic. Using our optimized SEIRD, we have obtained a Mean Squared Log Error of 10(-3) order, demonstrating the forecasts' elevated accuracy and reliability. In addition to forecasting the course of the pandemic for a 3 months season in all countries under investigation, we were able to estimate the transmission potential of COVID-19 represented by its effective reproduction number R-t. With R-t=1 is considered as the pandemic control threshold, it is evident that all of the countries under investigation are hovering just above the control threshold. This study might be relieving since it can demonstrate that the world is on the right track in terms of putting an end to the pandemic as soon as possible. The whole study shows how powerful is compartmental methods compared to classical statistical methods when used to model and forecast an infectious disease outbreak which encourages our further related research concerning the study of implementing advanced compartmental models considering additional parameters and controls.
