The CoViD-19 pandemic ceased to be describable by a susceptible-infected-recovered (SIR) model when lockdowns were enforced. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 (Sudden Acute Respiratory Syndrome Coronavirus 2) in terms of individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.