We introduce a simple compartmental model for the dynamics of a revolution in dictatorial regimes that employ censorship and police repression. A defining property of the model is the use of visibility and policing terms that feature rapid transitions as a function of the size of the revolution, for which we provide conceptual and network-based mathematical justifications. The complete mathematical classification of the dynamical behaviour of the model leads to a division in parameter space that is interpreted naturally in terms of stability of the regime (stable police state, meta-stable police state, unstable police state, and failed state). We show that these dynamical properties of the model are generic for a broad class of visibility and policing functions that feature rapid transitions. We investigate how the model can be applied to the peaceful revolutions of the Arab Spring in Tunisia and Egypt, taking into account the influence of the Internet and new media on the visibility of the revolution and the ensuing reduced effectivity of censorship. Within the model this leads to significant, discontinuous changes in regime stability, which greatly increase the probability of realized revolutions. These properties of the model inform possible answers to questions on causes and timing of the Arab Spring revolutions, and the role of the Internet and new media. The broader relevance of the model classification is also investigated by applying it to the current political situation in some other countries with regimes that employ censorship and police repression.