Continual learning, the ability of a model to learn over time without forgetting previous knowledge and, therefore, be adaptive to new data, is paramount in dynamic fields such as disease outbreak prediction. Deep neural networks, i.e., LSTM, are prone to error due to catastrophic forgetting. This study introduces a novel CEL model for continual learning by leveraging domain adaptation via Elastic Weight Consolidation (EWC). This model aims to mitigate the catastrophic forgetting phenomenon in a domain incremental setting. The Fisher Information Matrix (FIM) is constructed with EWC to develop a regularization term that penalizes changes to important parameters, namely, the important previous knowledge. CEL's performance is evaluated on three distinct diseases, Influenza, Mpox, and Measles, with different metrics. The high R-squared values during evaluation and reevaluation outperform the other state-of-the-art models in several contexts, indicating that CEL adapts to incremental data well. CEL's robustness and reliability are underscored by its minimal 65% forgetting rate and 18% higher memory stability compared to existing benchmark studies. This study highlights CEL's versatility in disease outbreak prediction, addressing evolving data with temporal patterns. It offers a valuable model for proactive disease control with accurate, timely predictions.