Low socio-economic status is associated with higher SARS-CoV-2 incidences. In this paper westudy whether this is a result of differences in (1) the frequency, (2) intensity, and/or (3) durationof local SARS-CoV-2 outbreaks depending on the local housing situations. So far, there is not clearevidence which of the three factors dominates. Using small-scale data from neighborhoods in theGerman city Essen and a flexible estimation approach which does not require prior knowledge aboutspecific transmission characteristics of SARS-CoV-2, behavioral responses or other potential modelparameters, we find evidence for the last of the three hypotheses. Outbreaks do not happen moreoften in less well-off areas or are more severe (in terms of the number of cases), but they last longer.This indicates that the socio-economic gradient in infection levels is at least in parts a result of a moresustained spread of infections in neighborhoods with worse housing conditions after local outbreaksand suggests that in case of an epidemic allocating scarce resources in containment measures to areaswith poor housing conditions might have the greatest benefit.