We set up a simple mathematical model for the dynamics of public interest in terms of media coverage and social interactions. We test the model on a series of events related to violence in the US during 2020, using the volume of tweets and retweets as a proxy of public interest, and the volume of news as a proxy of media coverage. The model succesfully fits the data and allows inferring a measure of social sensibility that correlates with human mobility data. These findings suggest the basic ingredients and mechanisms that regulate social responses capable of ignite social mobilizations.