A computer model is used to study recent experiments investigating laser-induced plasma formation and explosion of single liquid aerosol droplets. The model accounts for the formation and evolution of the plasma and the resulting fluid flow; it does not account for the initial breakdown. The model shows all the qualitative features of the experiment, including laser-supported detonation waves, which at high laser intensities rapidly convert the whole droplet into a plasma. In addition, quantitative agreement with measured velocities has been obtained to within approximately 50%.