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.