Abstract: A variety of models that capture the human circadian clock on a macroscopic level exist in the literature, and have been used effectively in predicting circadian phase for relatively normal or healthy subjects. Applying these models to more diverse populations with disrupted circadian phases (such as shift workers, cancer patients, and individuals with COVID-19) has been a recent and ongoing area of research. We extend these analyses by investigating the utility of mathematical models for circadian phase in different populations, working to develop algorithms for model individualization in order to enhance predictability, and using models in combination with machine learning to examine features changes in response to disease in differing subpopulations. In particular, we adapt limit-cycle oscillator models for circadian phase to provide accurate predictions based on real-world activity data, and quantify the effects of lighting schedules and parameters on the model outputs. We also develop novel algorithms for the analysis of wearable heart rate data, and apply these techniques to datasets from students, medical interns, and individuals with COVID-19. Through this framework we see changes to key physiologically-relevant parameters at different time points around COVID-19 symptom onset, thereby enhancing our understanding of disease progression and speaking to the potential of this analysis in early detection. Finally, we develop a real-time anomaly detection method based on a Kalman filter and autoencoder framework, and apply it to high-frequency oscillatory temperature data to detect anomalies prior to the traditional fever onset. These projects utilize tools from differential equations, mathematical modeling, circadian variation, and machine learning in order to generate meaningful additions to our understanding of personal health and disease status in the real-world.

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