Untangling lessons from the influenza’s plummeting during the COVID-19 pandemic is critical for mitigating seasonal and pandemic influenza. Here we explored a country-specific inference model to estimate the effects of mask-wearing, mobility changes (international and domestic) and SARS-CoV-2 interference in China, England and the United States. We found that mask wearing had a larger reduction than mobility changes in all the regions. Only in 2019-2020, SARS-CoV-2 interference had an observable effect, with values varying at the timing of the influenza season and the speed of SARS-CoV-2 community transmission. Compared to the epidemics in 2017–2019, longer and blunter rebounds could occur in the incoming 2021–2022 season, but the rebound would be smaller if less stringent mask mandates continued or the international mobility stayed low. Our results bear implications for understanding how influenza evolves under non-pharmaceutical interventions and other respiratory diseases, and will inform designing of tailored public health measures.