As a common phenomenon, overtaking behaviour is frequently observed on pedestrian flow, which not only reshapes pedestrian flow but also generates adverse impacts on pedestrian safety to some extent. Prior research focused on unidirectional pedestrian modelling, especially with overtaking behaviour, is limited. Moreover, pedestrian behaviour in the context of COVID-19 is rarely investigated. Inspired by the social force model, this paper proposes a dynamic sensitivity model for unidirectional pedestrian flow, which is able to describe the overtaking behaviour and analyse the potential impact of COVID-19 on pedestrian behaviour. In the proposed model, dynamic sensitivity and attention field of pedestrians are introduced to embody the effects of individual characteristics and surrounding environments on pedestrian behaviours. To calibrate the model and evaluate the effects of COVID-19 pandemic on pedestrian dynamics, real-life data collected by video recordings in Nanjing, China is used in this study. The simulation results indicate that the dynamic sensitivity model is able to reflect the variance of the adaptive velocity and route choice of overtaking pedestrians on unidirectional pedestrian flow. Our research findings show that the social distance during COVID-19 is higher than the value under normal conditions, and the majority of pedestrians tend to follow the suggested social distancing rules during COVID-19. Moreover, the overtaking pedestrians violate the suggested social distancing rules more frequently than the rest pedestrians.