Conventional computational modeling of sleep and arousal are primarily brain-centric in restricting attention to data from the nervous system. While such a view is warranted, the importance of considering the coupling of peripheral systems in the causes and effects of sleep are being increasingly recognized. An analysis is presented that has the capability to incorporate neural recordings of different modalities as well as data from the metabolic and immune systems. We formulate a matrix-based approach for inference of the arousal state based on the activity level of cell types that will comprise the matrix components. While the presented computations are intended to predict sleep/arousal, it is anticipated that a scrutiny of the structure of the matrices will provide insight into the dynamics of the constituent systems. A model is also proposed to consider the interaction of the signals recorded across the neural, metabolic, and immune systems in leading to the arousal state.