Mathematical models accurately simulate the effect of light on the human circadian rhythm: how can mathematical models of the effects of light on humans help us provide better lighting solutions?

Many biological processes in the body are governed by the circadian pacemaker located in the hypothalamus. We model the effect of light on this human circadian pacemaker based on two interacting processes: the internal clock (circadian rhythm) and the internal sleep drive (sleep homeostat). The biological processes are modeled mathematically using systems of coupled non-linear differential equations. Differences between individuals are expressed by model
parameters. Especially a person’s natural day length (tau) has a great influence on the model’s flow. Mathematical techniques, such as control theory, can be
used to analyze the model. Doing so, we will be able to use them to design smart lighting control systems that automatically adjust the light to achieve certain targets, such as jetlag compensation or mood improvement.