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Accurate forecasts of disease outbreaks are critical for effective public health responses, management of healthcare surge capacity, and communication of public risk. There are a growing number of powerful forecasting methods that fall into two broad categories-empirical models that extrapolate from historical data, and mechanistic models based on fixed epidemiological assumptions. However, these methods often underperform precisely when reliable predictions are most urgently needed-during periods of rapid epidemic escalation. Here, we introduce epimodulation, a hybrid approach that integrates fundamental epidemiological principles into existing predictive models to enhance forecasting accuracy, especially around epidemic peaks. When applied to empirical and machine learning forecasting methods (Autoregressive Integrated Moving Average, Holt-Winters, gradient-boosting machines, Prophet, and spline models), epimodulation improved overall prediction accuracy by an average of 12.3% (range: 8.5 to 18.7%) for COVID-19 hospital admissions and by 32.9% (range: 24.2 to 43.7%) for influenza hospital admissions; accuracy during epidemic peaks improved even further, by an average of 27.9% and 43.8%, respectively. Epimodulation also substantially enhanced the performance of complex forecasting methods, including the COVID-19 Forecast Hub ensemble model, demonstrating its broad utility in improving forecast reliability at critical moments in disease outbreaks.