The ability to accurately model and predict timing and duration of activities for different individuals is essential for successful and widespread Demand Side Response (DSR) policies, especially in the residential sector. Understanding what people do during the day and what factors influence their activity participation decisions is important for planning an effective DSR strategy to harness the end-user flexibility. The recent Covid-19 pandemic has shown how much activities can be shifted to a virtual mode in the presence of mobility restrictions. Further, participation in activities via digital devices (virtual activity participation) has spread across society. Such virtual activities, including teleworking, online shopping, and virtual social interactions, are observed to explicitly impact travel behaviour and activity scheduling. And yet, activity-based models of mobility and energy demand do not accommodate the trade-offs between activity types, location and virtual activity participation. This paper presents a model of activity participation that captures the relationship between the three dimensions of: activity type (such as work, study, shopping), activity location (in-home, out-of-home), and activity modality (in-person, virtual). A Multiple-Discrete Continuous Extreme Value (MDCEV) model structure is applied, and the empirical analysis is undertaken using the 2015 United Kingdom Time Use Survey (UKTUS). The model results provide insights for better understanding of the trade-offs made by individuals as they participate in and allocate time across a set of activity type-location-modality alternatives, and the heterogeneity in these trade-offs. Further, holdout sample validation and policy scenario analysis exercises are presented to demonstrate the reliability and suitability of the model for policy implications. The empirical results presented in our paper suggest that this framework embedded in an activity and agent-based simulator of energy demand will enable us to test a variety of scenarios related to end-user flexibility and activity behaviour change, including consideration of virtual activity participation trends.