Comparative Time Series Modeling of COVID-۱۹ and Vaccination Impact in India using SARIMAX and LSTM

The COVID-۱۹ pandemic has posed significant challenges to public health systems, highlighting the critical need for accurate and reliable forecasting models. This study presents a comparative analysis of a traditional statistical approach, Seasonal Autoregressive Integrated Moving Average (SARIMAX), and a deep learning model, Long Short-Term Memory (LSTM), for forecasting COVID-۱۹ dynamics in India. To enhance predictive performance, vaccination-related variables, including daily vaccinations and the number of fully vaccinated individuals, are incorporated as exogenous inputs, resulting in SARIMAX and multivariate LSTM frameworks. Daily time series data on new confirmed cases and deaths were analyzed using a structured preprocessing pipeline, stationarity testing, and rigorous train-test validation. Model performance was evaluated using Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE). The results demonstrate that the multivariate LSTM consistently outperforms the SARIMAX-based models, achieving a reduction in forecasting error of approximately ۱۵-۲۵% across key targets, particularly during periods of high volatility. These findings underscore the importance of integrating vaccination progress into epidemic forecasting models and highlight the superior capability of deep learning approaches in capturing non-linear dynamics. The proposed framework provides valuable insights for policymakers and public health authorities in managing large-scale infectious disease outbreaks in complex populations such as India.