After several weeks of "lockdown" as the sole answer to the COVID-19 pandemic, many countries are restarting their economic and social activities. However, balancing the re-opening of society against the implementation of non-pharmaceutical measures needed for minimizing interpersonal contacts requires a careful assessment of the risks of infection TRANS risks of infection TRANS infection MESHD as a function of the confinement relaxation strategies. Here, we present a stochastic coarse grained model that examines this problem. In our model, people are allowed to move between discrete positions on a one-dimensional grid with viral infection MESHD possible when two people are collocated at the same site. Our model features three sets of adjustable parameters, which characterize (i) viral transmission TRANS, (ii) viral detection, and (iii) degree of personal mobility, and as such, it is able to provide a qualitative assessment of the potential for second-wave infection MESHD outbreaks based on the timing, extent, and pattern of the lockdown relaxation strategy. In line with general expectations, our model predicts that a full lockdown yields the best results, namely, the lowest number of total infections MESHD. A less anticipated result was that when personal mobility is increased beyond a critical level, the risk of infection TRANS risk of infection TRANS infection MESHD rapidly reaches a constant value, which depends solely on the population density. Furthermore, according to our model, confinement alone is not effective if it is not accompanied by a detection capacity (coupled with quarantine) that surpasses 40% of the patients during their symptomatic phase. The results of our simulation also showed that keeping the virus transmission TRANS probability to less than 0.4, which can be achieved in real life by respecting social distancing or wearing masks, is as effective as imposing a mild lockdown. Finally, we note that detection and quarantine of pre-symptomatic patients, even with a probability as low as 0.2, would reduce the final numbers of infections MESHD by a factor of ten or more.