Multiscale Modeling of the Sleep/wake Systems

The mathematical modeling of biological processes is a powerful tool for informing both areas of mathematics and biology. Specifically the process of sleep deprivation has benefited from mathematical modeling, where researchers are not sure of many of the biological basis for the data. In our work, we successfully modeled the sleep/ wake system using the flip-flop switch formalism. Our model added on an aspect of the SCN, as the source of communication between the circadian and the neuronal sleep/ wake populations. Additionally, we took on the task of modeling sleep deprivation, both total and chronic. By introducing a constant, we were able to easily model total sleep deprivation so that it matched biological data. We found the process of modeling chronic sleep deprivation to be challenging and were able to contribute to the overall study of the differences between total and chronic sleep deprivation.