Is Gun Violence Contagious?
  Existing theories of gun violence predict stable spatial concentrations and contagious diffusion of gun violence into surrounding areas. Recent empirical studies have reported confirmatory evidence of such spatiotemporal diffusion of gun violence. However, existing tests cannot readily distinguish spatiotemporal clustering from spatiotemporal diffusion. This leaves as an open question whether gun violence actually is contagious or merely clusters in space and time. Compounding this problem, gun violence is subject to considerable measurement error with many nonfatal shootings going unreported to police. Using point process data from an acoustical gunshot locator system and a combination of Bayesian spatiotemporal point process modeling and space/time interaction tests, this paper demonstrates that contemporary urban gun violence does diffuse, but only slightly, suggesting that a disease model for infectious spread of gun violence is a poor fit for the geographically stable and temporally stochastic process observed. 
Charles Loeffler and Seth Flaxman
stat.AP