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We introduce EINNs, a framework crafted for epidemic forecasting that builds upon the theoretical grounds provided by mechanistic models as well as the data-driven expressibility afforded by AI models, and their capabilities to ingest heterogeneous information. Although neural forecasting models have been successful in multiple tasks, predictions well-correlated with epidemic trends and long-term predictions remain open challenges. Epidemiological ODE models contain mechanisms that can guide us in these two tasks; however, they have limited capability of ingesting data sources and modeling composite signals. Thus, we propose to leverage work in physics-informed neural networks to learn latent epidemic dynamics and transfer relevant knowledge to another neural network which ingests multiple data sources and has more appropriate inductive bias. In contrast with previous work, we do not assume the observability of complete dynamics and do not need to numerically solve the ODE equations during training. Our thorough experiments on all US states and HHS regions for COVID-19 and influenza forecasting showcase the clear benefits of our approach in both short-term and long-term forecasting as well as in learning the mechanistic dynamics over other non-trivial alternatives. 

Healthcare acquired infections (HAIs) (e.g., Methicillin-resistant Staphylococcus aureus infection) have complex transmission pathways, spreading not just via direct person-to-person contacts, but also via contaminated surfaces. Prior work in mathematical epidemiology has led to a class of models – which we call load sharing models – that provide a discrete-time, stochastic formalization of HAI-spread on temporal contact networks. The focus of this paper is the source detection problem for the load sharing model. The source detection problem has been studied extensively in SEIR type models, but this prior work does not apply to load sharing models.We show that a natural formulation of the source detection problem for the load sharing model is computationally hard, even to approximate. We then present two alternate formulations that are much more tractable. The tractability of our problems depends crucially on the submodularity of the expected number of infections as a function of the source set. Prior techniques for showing submodularity, such as the "live graph" technique are not applicable for the load sharing model and our key technical contribution is to use a more sophisticated "coupling" technique to show the submodularity result. We propose algorithms for our two problem formulations by extending existing algorithmic results from submodular optimization and combining these with an expectation propagation heuristic for the load sharing model that leads to orders-of-magnitude speedup. We present experimental results on temporal contact networks based on fine-grained EMR data from three different hospitals. Our results on synthetic outbreaks on these networks show that our algorithms outperform baselines by up to 5.97 times. Furthermore, case studies based on hospital outbreaks of Clostridioides difficile infection show that our algorithms identify clinically meaningful sources.