An accurate and timely estimate of the reproduction ratio R of an infectious disease epidemic is crucial to make projections on its evolution and set up the appropriate public health response. Estimates of R routinely come from statistical inference on timelines of cases or their proxies like symptomatic cases, hospitalizatons, deaths. Here, however, we prove that these estimates of R may not be accurate if the population is made up of spatially distinct communities, as the interplay between space and mobility may hide the true epidemic evolution from surveillance data. This means that surveillance may underestimate R over long periods, to the point of mistaking a growing epidemic for a subsiding one, misinforming public health response. To overcome this, we propose a correction to be applied to surveillance data that removes this bias and ensures an accurate estimate of R across all epidemic phases. We use COVID-19 as case study; our results, however, apply to any epidemic where mobility is a driver of circulation, including major challenges of the next decades: respiratory infections (influenza, SARS-CoV-2, emerging pathogens), vector-borne diseases (arboviruses). Our findings will help set up public health response to these threats, by improving epidemic monitoring and surveillance.