The time-varying reproduction (Rt) provides a real-time estimate of pathogen transmissibility and may be influenced by exogenous factors such as mobility and mitigation measures which are not directly related to epidemiology parameters and observations. Meanwhile, evaluating the impacts of these factors is vital for policy makers to propose and adjust containment strategies. Here, we developed a Bayesian regression framework, EpiRegress, to provide Rt estimates and assess impacts of diverse factors on virus transmission, utilising daily case counts, mobility, and policy data. To demonstrate the method’s utility, we used simulations as well as data in four regions from the Western Pacific with periods of low COVID-19 incidence, namely: New South Wales, Australia; New Zealand; Singapore; and Taiwan, China. We found that imported cases had a limited contribution on the overall epidemic dynamics but may degrade the quality of the Rt estimate if not explicitly accounted for. We additionally demonstrated EpiRegress’s capability in nowcasting disease transmissibility before contemporaneous cases diagnosis. The approach was proved flexible enough to respond to periods of atypical local transmission during epidemic lulls and to periods of mass community transmission. Furthermore, in epidemics where travel restrictions are present, it is able to distinguish the influence of imported cases.