Road closure is an effective measure to reduce mobility and prevent the spread of an epidemic in severe public health crises. For instance, during the peak waves of the global COVID-19 pandemic, many countries implemented road closure policies, such as the traffic-calming strategy in the UK. However, it is still not clear how such road closures, if used as a response to different modes of epidemic spreading, affect the resilient performance of large-scale road networks in terms of their efficiency and overall accessibility. In this paper, we propose a simulation-based approach to theoretically investigate two types of spreading mechanisms and evaluate the effectiveness of both static and dynamic response scenarios, including the sporadic epidemic spreading based on network topologies and trajectory-based spreading caused by superspreaders in megacities. The results showed that (1) the road network demonstrates comparatively worse resilient behavior under the trajectory-based spreading mode; (2) the road density and centrality order, as well as the network's regional geographical characteristics, can substantially alter the level of impacts and introduce heterogeneity into the recovery processes; and (3) the resilience lost under static recovery and dynamic recovery scenarios is 8.6 and 6.9%, respectively, which demonstrates the necessity of a dynamic response and the importance of making a systematic and strategic recovery plan. Policy and managerial implications are also discussed. This paper provides new insights for better managing the resilience of urban road networks against public health crises in the post-COVID era.