Even during sustained attention, enhanced processing of attended stimuli waxes and wanes rhythmically, with periods of enhanced and relatively diminished visual processing (and subsequent target detection) alternating at 4 or 8 Hz in a sustained visual attention task. These alternating attentional states occur alongside alternating dynamical states, in which lateral intraparietal cortex (LIP), the frontal eye field (FEF), and the mediodorsal pulvinar (mdPul) exhibit different activity and functional connectivity at α, β, and γ frequencies-rhythms associated with visual processing, working memory, and motor suppression. To assess whether and how these multiple interacting rhythms contribute to periodicity in attention, we propose a detailed computational model of FEF and LIP. When driven by θ-rhythmic inputs simulating experimentally-observed mdPul activity, this model reproduced the rhythmic dynamics and behavioral consequences of observed attentional states, revealing that the frequencies and mechanisms of the observed rhythms allow for peak sensitivity in visual target detection while maintaining functional flexibility.