In addition to controlling the influx of light to the retina, the pupil also reacts as a result of cognitive and emotional processing. This makes it possible to use pupil dilation as an index for cognitive effort and emotional arousal. We show how an extended version of a computational model of pupil dilation can account for pupillary contagion effects where the pupil of an observer dilates upon seeing another person with dilated pupils. We also show how the model can reproduce the effects of cognitive effort in a math exercise. Furthermore, we investigate how the model can account for different explanations for the abnormal pupil response seen in individuals with or at risk for autism spectrum disorder. The reported computer simulations illustrate the usefulness of system-level models of the brain in addressing complex cognitive and emotional phenomena.