When considering airborne epidemic spreading in social systems, a natural connection arises between mobility and epidemic contacts. As individuals travel, possibilities to encounter new people either at the final destination or during the transportation process appear. Such contacts can lead to new contagion events. In fact, mobility has been a crucial target for early non-pharmaceutical containment measures against the recent COVID-19 pandemic, with a degree of intensity ranging from public transportation line closures to regional, city or even home confinements. Nonetheless, quantitative knowledge on the relationship between mobility-contagions and, consequently, on the efficiency of containment measures remains elusive. Here we introduce an agent-based model with a simple interaction between mobility and contacts. Despite its simplicity our model shows the emergence of a critical mobility level, inducing major outbreaks when surpassed. We explore the interplay between mobility restrictions and the infection in recent intervention policies seen across many countries, and how interventions in the form of closures triggered by incidence rates can guide the epidemic into an oscillatory regime with recurrent waves. We consider how the different interventions impact societal well-being, the economy and the population. Finally, we propose a mitigation framework based on the critical nature of mobility in an epidemic, able to suppress incidence and oscillations at will, preventing extreme incidence peaks with potential to saturate health care resources.

13 pages, 5 figures