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A multi-modal transport system is acknowledged to have robust failure tolerance and can effectively relieve urban congestion issues. However, estimating the impact of disruptions across multi-transport modes is a challenging problem due to a dis-aggregated modelling approach applied to only individual modes at a time. To fill this gap, this paper proposes a new integrated modelling framework for a multi-modal traffic state estimation and evaluation of the disruption impact across all modes under various traffic conditions. First, we propose an iterative trip assignment model to elucidate the association between travel demand and travel behaviour, including a multi-modal origin-to-destination estimation for private and public transport. Secondly, we provide a practical multi-modal travel demand re-adjustment that takes the mode shift of the affected travellers into consideration. The pros and cons of the mode shift strategy are showcased via several scenario-based transport simulating experiments. The results show that a well-balanced mode shift with flexible routing and early announcements of detours so that travellers can plan ahead can significantly benefit all travellers by a delay time reduction of 46%, while a stable route assignment maintains a higher average traffic flow and the inactive mode-route choice help relief density under the traffic disruptions.