Economic geography, statistical and mathematical modelling of spatial processes, and applications to problems in location theory and spatial diffusion. The geographical spread of human diseases and the demographical implications have been a special focus.

Andrew Cliff's earliest research was on spatial statistics. This work, with J.K.Ord, examines spatial processes for marked and unmarked point patterns, and appears in Spatial Autocorrelation (1973) and Spatial Processes (1981).

His current research focuses on applications of spatial diffusion models to the spread of epidemic diseases. Predicting the spatial spread of childhood diseases such as measles with a view to devising control strategies has been a central theme. Isolated island communities such as Iceland and the Pacific island groups have been important test-beds for trying out the forecasting models.

The work has identified the geographical factors which cause diseases to be endemic or epidemic in different locations, showing that disease levels are influenced by population density, vaccination intensity and degree of population flux. In particular, once the population size of an area falls below certain threshold densities which vary over time and space, the disease concerned is eventually extinguished, and it can only recur by re-introduction from other areas where the disease is permanently present. Thus the generalized persistence of disease implies geographical transmission between regions.