Predicting COVID-19 pandemic waves with biologically and behaviorally informed universal differential equations

Abstract In the early stages of the COVID-19 pandemic, it became clear that pandemic waves and population responses were locked in a mutual feedback loop. The initial lull following strict interventions in the first wave often led to a second wave, as restrictions were relaxed. We test the ability of new hybrid machine learning techniques, namely universal differential equations (UDEs) with learning biases, to make predictions in a such a dynamic behavior-disease setting. We develop a UDE model for COVID-19 and test it both with and without learning biases describing simple assumptions about disease transmission and population response. Our results show that UDEs, particularly when supplied with learning biases, are capable of learning coupled behavior-disease dynamics and predicting second waves in a variety of populations. The model predicts a second wave of infections 55% of the time across all populations, having been trained only on the first wave. The predicted second wave is larger than the first. Without learning biases, model predictions are hampered: the unbiased model predicts a second wave only 25% of the time, typically smaller than the first. The biased model consistently predicts the expected increase in the transmission rate with rising mobility, whereas the unbiased model predicts a decrease in mobility as often as a continued increase. The biased model also achieves better accuracy on its training data thanks to fewer and less severely divergent trajectories. These results indicate that biologically informed machine learning can generate qualitatively correct mid to long-term predictions of COVID-19 pandemic waves. Significance statement Universal differential equations are a relatively new modelling technique where neural networks use data to learn unknown components of a dynamical system. We demonstrate for the first time that this technique is able to extract valuable information from data on a coupled behaviour-disease system. Our model was able to learn the interplay between COVID-19 infections and time spent travelling to retail and recreation locations in order to predict a second wave of cases, having been trained only on the first wave. We also demonstrate that adding additional terms to the universal differential equation’s loss function that penalize implausible solutions improves training time and leads to improved predictions.

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