Researchers at Surrey University have developed and tested a variant of the Epidemic Type Aftershock Sequence (ETAS) model to apply to urban crime data (Jul 2018). Testing mostly has been done on US gang data. The model assumes historical trends at a location to some extent influence future events at that location.

Mathematically, this combines a cell-based fixed grid (150 x150) representing geographical locations with time-series analysis of historical data for each cell to predict near future crime levels as hot spots. The time series analysis  is done by fitting a self-exciting rate process (Hawkes) to provide data for directing police resources in real time.

The details of the analysis are at:

A significant weakness in their model is the lack of inclusion of geographical juxtaposition effects by which crime activity in nearby locations (cells) have influence more broadly. Currently, in their model, this criminogenic aspect has been assumed into each cell's history. That is, relationship effects are assumed linear locationally and that higher derivative effects are negligible. In fact, evidence indicates that effects from higher derivative influences are significant. A practical example is when territorial gang disputes result in changes to gang territory boundaries and hence break the pattern of historical influence per cell.