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Since the end of 2019, a novel coronavirus known as COVID-19 has caused a severe outbreak worldwide. Due to the complexity of epidemic data, traditional algorithms have struggled to accurately predict the development of the pandemic. The Autoregressive Integrated Moving Average (ARIMA) model is capable of capturing time-based trends in epidemic data, including seasonality, cyclic patterns, and long-term trends, which helps improve the accuracy of forecasting future epidemic trajectories. The Bidirectional Long Short-Term Memory (BiLSTM) network, a variant of the Recurrent Neural Network (RNN), is highly effective in handling sequential data. In epidemic data analysis, BiLSTM models can be applied to forecast future trends or conduct time series predictions. BiLSTM is able to capture temporal relationships and sequential patterns within data, thereby providing more accurate predictions. Genetic Algorithms (GA), inspired by biological evolution through operations such as selection, crossover, and mutation, offer an efficient approach to identifying the best-fit models and parameter configurations. By using GA, we can iteratively optimize epidemic forecasting models and enhance their performance over time. In this study, we proposed a hybrid model called GA-BiLSTM-ARIMA. Using COVID-19 case data from Japan, we calculated the GA-BiLSTM-ARIMA model's evaluation metrics: RMSE, MAE, MAPE, and R ², which were 2,262.42, 1,672.07, 6.81, and 0.9764, respectively. The results demonstrate that the hybrid model outperforms both the standalone BiLSTM and ARIMA models in predictive performance. The GA-BiLSTM-ARIMA model successfully integrates the strengths of different models through a systematic and intelligently optimized hybrid strategy. When forecasting infectious disease time series data, this model achieves higher and more robust predictive accuracy compared to traditional single models or partial hybrid models. This type of analysis supports the development of more effective prevention and control strategies and delivers accurate information and early warnings to the public and policymakers, contributing to a better global response to pandemic challenges.