**Project leader: **Professor **Xiuyuan Cheng****Project manager: **Yixuan Tan**Team members: **Brian Lee, Flora Shi, Nick Talati

Understanding the spread of disease is extremely important for public health and policymaking. An epidemic is just one example of a spatial temporal phenomenon–meaning that over time, a disease spreads across space. We simulate the spread of an epidemic using a stochastic SEIR model, which describes how people transition from being susceptible to a disease, to exposed, to infected, and to recovered. We also adapt this model for populations represented by graphs by simulating movement between nearby regions (nodes) over the course of the simulated epidemic. We analyze the predictive performance of several different artificial intelligence models (all neural networks) on simulated epidemics. Importantly, we modify standard recurrent neural networks to allow them to preserve information about the graph on which the epidemic simulation took place. We also demonstrate the predictive performance of these models on real world data.

The SEIR model for epidemics describes the spread of disease through a system of ordinary differential equations. In the stochastic version of the model, transitions between the four compartments (S, E, I, and R) are determined by Poisson processes; furthermore, a combination of the stochastic SEIR model and graph diffusion can be used to model the spread of disease on a graph (where each node can represent countries, cities, etc.). Recurrent neural networks (RNNs), including long short-term memory networks (LSTMs), are the most common tool used to make predictive forecasts on time-series data. However, when predicting on a graph signal these networks do not utilize the spatial information encoded in the graph’s edges. We modify RNNs and LSTMs by integrating graph convolutional operations into the networks, thereby allowing the entire graph to be included as input to the neural networks, and thus preserving important spatial information. We test the predictive performance of these modified RNNs and LSTMs as compared to standard RNNs and LSTMs on data simulated using the stochastic SEIR model on graphs.