This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: "Upset" (U), "Violent" (V), "Sensitive" (S), "Immune" (I), and "Relaxed" (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed a new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent world violent events are discussed.