Mathematical Modeling to Predict COVID-19 Infection and Vaccination Trends

Background: COVID-19 caused by the Severe Acute Respiratory Syndrome Coronavirus 2 placed the health systems around the entire world in a battle against the clock. While most of the existing studies aimed at forecasting the infections trends, our study focuses on vaccination trend(s). Material and methods: Based on these considerations, we used standard analyses and ARIMA modeling to predict possible scenarios in Romania, the second-lowest country regarding vaccinations from the entire European Union. Results: With approximately 16 million doses of vaccine against COVID-19 administered, 7,791,250 individuals had completed the vaccination scheme. From the total, 5,058,908 choose Pfizer–BioNTech, 399,327 Moderna, 419,037 AstraZeneca, and 1,913,978 Johnson & Johnson. With a cumulative 2147 local and 17,542 general adverse reactions, the most numerous were reported in recipients of Pfizer–BioNTech (1581 vs. 8451), followed by AstraZeneca (138 vs. 6033), Moderna (332 vs. 1936), and Johnson & Johnson (96 vs. 1122). On three distinct occasions have been reported >50,000 individuals who received the first or second dose of a vaccine and >30,000 of a booster dose in a single day. Due to high reactogenicity in case of AZD1222, and time of launching between the Pfizer–BioNTech and Moderna vaccine could be explained differences in terms doses administered. Furthermore, ARIMA(1,1,0), ARIMA(1,1,1), ARIMA(0,2,0), ARIMA(2,1,0), ARIMA(1,2,2), ARI-MA(2,2,2), ARIMA(0,2,2), ARIMA(2,2,2), ARIMA(1,1,2), ARIMA(2,2,2), ARIMA(2,1,1), ARIMA(2,2,1), and ARIMA (2,0,2) for all twelve months and in total fitted the best models. These were regarded according to the lowest MAPE, p-value (p < 0.05, p < 0.01, and p < 0.001) and through the Ljung–Box test (p < 0.05, p < 0.01, and p < 0.001) for autocorrelations. Conclusions: Statistical modeling and mathematical analyses are suitable not only for forecasting the infection trends but the course of a vaccination rate as well.