Connecting dynamic models with data to yield predictive results often requires a variety of parameter estimation, identifiability, and uncertainty quantification techniques. These approaches can help to determine what is possible to estimate from a given model and data set, and help guide new data collection. Here, we examine how parameter estimation and disease forecasting are affected when examining disease transmission via multiple types or pathways of transmission. Using examples taken from the West Africa Ebola epidemic, HPV, and cholera, we illustrate some of the potential difficulties in estimating the relative contributions of different transmission pathways, and show how alternative data collection may help resolve this unidentifiability. We also illustrate how even in the presence of large uncertainties in the data and model parameters, it may still be possible to successfully forecast disease dynamics.

Circadian clocks persist with a constant period (~24-hour) even after a significant change of the expression level of clock genes. To study the biochemical mechanisms of timekeeping, we develop the most accurate mathematical model of mammalian intracellular timekeeping, as well as a simplified model amenable to mathematical analysis. This modeling work raises interesting questions about existence and uniqueness of models given knowledge of their solutions. Although much is known about cellular circadian timekeeping, little is known about how these rhythms are sustained with a constant period. Here, we show how a universal motif of circadian timekeeping, where repressors bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. Furthermore, we find that, even in the presence of large changes in gene expression levels, an additional slow negative feedback loop keeps this stoichiometry in balance and maintains oscillations with a fixed period. These results explain why the network structure found naturally in circadian clocks can generate ~24-hour oscillations in many conditions.