A physiologically based mathematical model of sleep-wake cycles is used to examine the effects of shift rotation interval (RI) (i.e., the number of days spent on each shift) on sleepiness and circadian dynamics on forward rotating 3-shift schedules. The effects of the schedule start time on the mean shift sleepiness are also demonstrated but are weak compared to the effects of RI. The dynamics are studied for a parameter set adjusted to match a most common natural sleep pattern (i.e., sleep between 0000 and 0800) and for common light conditions (i.e., 350 lux of shift lighting, 200 lux of daylight, 100 lux of artificial lighting during nighttime, and 0 lux during sleep). Mean shift sleepiness on a rotating schedule is found to increase with RI, reach maximum at intermediate RI=6 d, and then decrease. Complete entrainment to shifts within the schedules is not achieved at RI≤10 d. However, circadian oscillations synchronize to the rotation cycles, with RI=1,2 d and RI≥6 d demonstrating regular periodic changes of the circadian rhythm. At rapid rotation, circadian phase stays within a small 4-h interval, whereas slow rotation leads to around-the-clock transitions of the circadian phase with constantly delayed sleep times. Schedules with RI=3-5 d are not able to entrain the circadian rhythms, even in the absence of external circadian disturbances like social commitments and days off. To understand the circadian dynamics on the rotating shift schedules, a shift response map is developed, showing the direction of circadian change (i.e., delay or advance) depending on the relation between the shift start time and actual circadian phase. The map predicts that the un-entrained dynamics come from multiple transitions between advance and delay behavior on the shifts in the schedules. These are primarily caused by the imbalance between the amount of delay and advance on the different shift types within the schedule. Finally, it is argued that shift response maps can aid in the development of shift schedules with desired circadian characteristics.
