Traffic forecasting is an important problem in the operation and optimisation of transportation systems. State-of-the-art solutions train machine learning models by minimising the mean forecasting errors on the training data. The trained models often favour periodic events instead of aperiodic ones in their prediction results, as periodic events often prevail in the training data. While offering critical optimisation opportunities, aperiodic events such as traffic incidents may be missed by the existing models. To address this issue, we propose DualCast -- a model framework to enhance the learning capability of traffic forecasting models, especially for aperiodic events. DualCast takes a dual-branch architecture, to disentangle traffic signals into two types, one reflecting intrinsic {spatial-temporal} patterns and the other reflecting external environment contexts including aperiodic events. We further propose a cross-time attention mechanism, to capture high-order spatial-temporal relationships from both periodic and aperiodic patterns. DualCast is versatile. We integrate it with recent traffic forecasting models, consistently reducing their forecasting errors by up to 9.6% on multiple real datasets.