Explaining COVID-19 outbreaks with reactive SEIRD models

COVID-19 epidemics have varied dramatically in nature across the United States, where some counties have clear peaks in infections, and others have had a multitude of unpredictable and non-distinct peaks. Our lack of understanding of how the pandemic has evolved leads to increasing errors in our ability to predict the spread of the disease. This work seeks to explain this diversity in epidemic progressions by considering an extension to the compartmental SEIRD model. The model we propose uses a neural network to predict the infection rate as a function of both time and the disease’s prevalence. We provide a methodology for fitting this model to available county-level data describing aggregate cases and deaths. Our method uses Expectation-Maximization to overcome the challenge of partial observability, due to the fact that the system’s state is only partially reflected in available data. We fit a single model to data from multiple counties in the United States exhibiting different behavior. By simulating the model, we show that it can exhibit both single peak and multi-peak behavior, reproducing behavior observed in counties both in and out of the training set. We then compare the error of simulations from our model with a standard SEIRD model, and show that ours substantially reduces errors. We also use simulated data to compare our methodology for handling partial observability with a standard approach, showing that ours is significantly better at estimating the values of unobserved quantities.

State-Based Recurrent SPMNs for Decision-Theoretic Planning under Partial Observability

The sum-product network (SPN) has been extended to model sequence data with the recurrent SPN (RSPN), and to decision-making problems with sum-product-max networks (SPMN). In this paper, we build on the concepts introduced by these extensions and present state-based recurrent SPMNs (S-RSPMNs) as a generalization of SPMNs to sequential decision-making problems where the state may not be perfectly observed. As with recurrent SPNs, S-RSPMNs utilize a repeatable template network to model sequences of arbitrary lengths. We present an algorithm for learning compact template structures by identifying unique belief states and the transitions between them through a state matching process that utilizes augmented data. In our knowledge, this is the first data-driven approach that learns graphical models for planning under partial observability, which can be solved efficiently. S-RSPMNs retain the linear solution complexity of SPMNs, and we demonstrate significant improvements in compactness of representation and the run time of structure learning and inference in sequential domains.