The novel coronavirus (COVID-19), also known as SARS-CoV-2, is a highly contagious respiratory disease that first emerged in Wuhan, China in 2019 and has since become a global pandemic. The virus is spread through respiratory droplets produced when an infected person coughs or sneezes, and it can lead to a range of symptoms, from mild to severe. Some people may not have any symptoms at all and can still spread the virus to others. The best way to prevent the spread of COVID-19 is to practice good hygiene. It is also important to follow the guidelines set by local health authorities, such as physical distancing and quarantine measures. The World Health Organization (WHO), on the other hand, has classified this virus as a pandemic, and as a result, all nations are attempting to exert control and secure all public spaces. The current study aimed to (I) compare the weekly COVID-19 cases between Israel and Greece, (II) compare the monthly COVID-19 mortality cases between Israel and Greece, (III) evaluate and report the influence of the vaccination rate on COVID-19 mortality cases in Israel, and (IV) predict the number of COVID-19 cases in Israel. The advantage of completing these tasks is the minimization of the spread of the virus by deploying different mitigations. To attain our objective, a correlation analysis was carried out, and two distinct artificial intelligence (AI)-based models—specifically, an artificial neural network (ANN) and a classical multiple linear regression (MLR)—were developed for the prediction of COVID-19 cases in Greece and Israel by utilizing related variables as the input variables for the models. For the evaluation of the models, four evaluation metrics (determination coefficient (R2), mean square error (MSE), root mean square error (RMSE), and correlation coefficient (R)) were considered in order to determine the performance of the deployed models. From a variety of perspectives, the corresponding determination coefficient (R2) demonstrated the statistical advantages of MLR over the ANN model by following a linear pattern. The MLR predictive model was both efficient and accurate, with 98% accuracy, while ANN showed 94% accuracy in the effective prediction of COVID-19 cases.