Illness signatures are mathematically characterized by entrainment relationships among multiple time series representations of physiological processes. Such characteristics include time and phase lags, window lengths for optimum detection, which time series are most entrained with each other, the degree of entrainment relative to the rest of the large database, and the concordance or discordance of the time-varying changes. These optimum disease-specific characteristics can be determined, for example, from large, clinically well-annotated databases of time series representations of physiological processes during health and illness. These characteristics of the entrainment relationships among multiple time series representations of physiological processes are used to make mathematical and statistical predictive models using multivariable techniques such as, but not limited to, logistic regression, nearest-neighbor techniques, neural and Bayesian networks, principal and other component analysis, and others. These models are quantitative expressions that transform measured characteristics to the probability of an illness, or p(illness).