  We have two main aims in this paper. First we use theories of disease
spreading on networks to look at the COVID-19 epidemic on the basis of
individual contacts -- these give rise to predictions which are often rather
different from the homogeneous mixing approaches usually used. Our second aim
is to look at the role of social deprivation, again using networks as our
basis, in the spread of this epidemic. We choose the city of Kolkata as a case
study, but assert that the insights so obtained are applicable to a wide
variety of urban environments which are densely populated and where social
inequalities are rampant. Our predictions of hotspots are found to be in good
agreement with those currently being identifed empirically as containment zones
and provide a useful guide for identifying potential areas of concern.
