Modeling the social-spatial structure of urban spaces can facilitate the development of guidelines aimed at curbing the spread of the COVID-19 pandemic while also acting as an instrument that helps decision-making concerning mitigation policies. The modeling process starts with categorization of urban spaces based on the concept of social vulnerability. A model is created based on this concept and the theory of analysis of social areas. Statistical techniques of factor analysis and geostatistics are applied. This generates a map of social differentiation that, when related to data on the evolution of the contagion, generates a multidimensional model of social vulnerability. The application of this model towards people (social structure) and the environment where they live (spatial structure) is specified. Our model assumes the uniqueness of cities, and it is intended to be a broadly applicable model that can be extrapolated to other urban areas if pertinent revisions are made. Our work demonstrates that aspects of the social and urban structures may be validly used to analyze and explain the spatial spread of COVID-19.