Using the synthesis and degradation rates of their mRNAs, which were measured in vitro, we showed that the current mathematical model is not sufficient to reproduce the phase difference between Per1 and Per2. Therefore, we predicted that an additional feedback regulation contributed to the phase difference. In the model that included positive feedback regulation of Per2, newly synthesized PER1/2 enhanced Per2 transcription following transactivation by CLOCK-BMAL1 and caused the delay of the transcriptional peak. More importantly, this model produced the phase lag with a slight alteration in the oscillation period, and the extent of the phase delay of Per2 was dependent on factors that affected the intensity of positive feedback regulation, such as the abundance of PER1/2. In addition, the circadian expressions of all genes involved in our model could be entrained to 12 h:12 h LD cycles in which Per1 and Per2 transcription rate coefficients were varied in a 24-hour period square-wave manner. Significantly, the phase of Per2 transcription also lagged behind that of Per1 in this condition. In contrast, one of three alternative models, which included Per1 transcriptional repression by PER1/ 2, could simulate the phase advance of Per1, but this advance was not ahead of the Per2 oscillation phase. The Per2 oscillation was almost in phase with nuclear BMAL1 oscillation in the model, which implemented the synthesis and degradation rates as estimated in vitro, so Per1 oscillation needed to be ahead of BMAL1 oscillation to be ahead of Per2 oscillation. If transcriptional repression by PER1/2 surpasses CLOCK-BMAL1 transactivity at the midpoint or later SB-668875 within its phase, the oscillation phase of Per1 is advanced over the peak phase of CLOCK-BMAL1. However, an increase of negative feedback strength of Per1 transcription led to a decrease of PER1 protein expression, and our model did not simulate the PF-06761281 expression pattern of nuclear PER1/2 that meets the requirement. Besides, the observed Per1 mRNA oscillation is not ahead of BMAL1 protein expression peak. National and regional estimates of the weekly percentage of persons seeking health care. The remaining surveillance data were obtained from CDC.