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Neural differential equations and deep learning from data to inform unknown behavior adaption during outbreaks of emerging infectious diseases
Descriptions of differential equations governing the dynamical behaviors of systems often involve unknown mechanisms, as illustrated by the epidemic models designed to depict and predict the outbreak trend of an emerging infectious disease when population adjusts their social contacts in respond to real and perceived infection risks. How to inform the mechanisms of behavioural adaption from real-time public health surveillance data in order to provide reliable prediction of epidemic trends has been a challenge in outbreak and pandemic modeling. In a recent series of studies in collaboration with Pengfei Song and Yanni Xiao, we developed a method to represent optimal control functions relevant to data fitting by neural networks, solve optimal control problems by deep learning techniques, and apply adjoint sensitivity analyses to train the neural networks embedded in differential equations. The method is used to estimate model parameters in classic epidemic control problems, to discover unknown mechanisms including behavioural changes, and to gain new insights into different realizations of disease outbreaks.