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Infectious human diseases are often characterized by seasonal variation in incidence which produces recurring annual peaks with precise timing. Changing weather conditions such as temperature and humidity are known to affect virus transmission, but we consider the possibility that an intrinsic rhythm in susceptibility, entrained to annual cues, also contributes to seasonality. These two mechanisms produce different predictions about how the timing and amplitude of seasonal disease depend on environmental forcing. Using databases of health insurance claims and weather across U.S. counties, we find that the timing of winter-peaking diseases, but not their amplitude, scales with latitude. This latitude scaling is shared across many diagnosis codes involving multiple pathogens. Regression against simple models suggests an underlying limit cycle that, in temperate zones, is entrained to annual changes in irradiance, possibly a human circannual clock.