Sleep alteration in the van der Pol-type circadian pacemaker model driven by natural light and intermittent noise

Sleep/wake cycles were once dictated by the solar day, but now humans are subjected to prolonged exposure to artificial light, resulting in altered daily sleep patterns. We investigate a van der Pol-type mathematical model for a circadian model, which incorporates a daylight and noise model, to capture the consequences of artificial light, which has become part of our daily lives. The results show that when the cycle is interpreted as a model for the sleep/awake alternation, the duration and sleep offset are influenced by light intensity, daylight duration and noise intensity. Increasing light intensity and duration can lead to a decrease in sleep duration beyond ∼30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 30$$\end{document} mins. Thus, the cycle of the circadian oscillations can be influenced by a sudden change in longitude (jet lag) is much more influenced by the daily duration of light than by its intensity. Noise could cause a loss of sleep of more than 10%; in other words, artificial light could cause a decrease of more than 40 min in sleep time, which could cause a malfunction of the human mechanism. Furthermore, simulations show that the duration of sleep during the different seasons of the year reveals that it is in winter that sleep is longer in contrast to summer where the daily loss of sleep could be as much as 5% (∼20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim 20$$\end{document} mins); nevertheless, the increase in noise intensity can decrease the duration of sleep in winter and make it shorter than in summer. The evolution of light over the year is slow enough for the oscillator to regulate sleep time, whereas a sudden change in latitude and the consequent change in daily light could cause major dysfunctions on sleep time and requires an adaptation time to be regulated; Indeed the adaptation to this change could take several cycles and depends on the environmental conditions, as it would be more difficult for the organism to regulate its sleep if moving from a point with long daylight to a position with shorter daylight than for a trip in the opposite direction. In brief, the mathematical van der Pol pacemaker model of the circadian rhythm driven by periodic and random terms, that mimic realistic illumination, provides quantitative information on alterations in the circadian sleep/wake pattern, in agreement with empirical observations.