  Modeling the spatiotemporal nature of the spread of infectious diseases can
provide useful intuition in understanding the time-varying aspect of the
disease spread and the underlying complex spatial dependency observed in
people's mobility patterns. Besides, the county level multiple related time
series information can be leveraged to make a forecast on an individual time
series. Adding to this challenge is the fact that real-time data often deviates
from the unimodal Gaussian distribution assumption and may show some complex
mixed patterns. Motivated by this, we develop a deep learning-based time-series
model for probabilistic forecasting called Auto-regressive Mixed Density
Dynamic Diffusion Network(ARM3Dnet), which considers both people's mobility and
disease spread as a diffusion process on a dynamic directed graph. The Gaussian
Mixture Model layer is implemented to consider the multimodal nature of the
real-time data while learning from multiple related time series. We show that
our model, when trained with the best combination of dynamic covariate features
and mixture components, can outperform both traditional statistical and deep
learning models in forecasting the number of Covid-19 deaths and cases at the
county level in the United States.
