  We present an Extended Kalman Filter framework for system identification and
control of a stochastic high-dimensional epidemic model. The scale and severity
of the COVID-19 emergency have highlighted the need for accurate forecasts of
the state of the pandemic at a high resolution. Mechanistic compartmental
models are widely used to produce such forecasts and assist in the design of
control and relief policies. Unfortunately, the scale and stochastic nature of
many of these models often makes the estimation of their parameters difficult.
With the goal of calibrating a high dimensional COVID-19 model using low-level
mobility data, we introduce a method for tractable maximum likelihood
estimation that combines tools from Bayesian inference with scalable
optimization techniques from machine learning. The proposed approach uses
automatic backward-differentiation to directly compute the gradient of the
likelihood of COVID-19 incidence and death data. The likelihood of the
observations is estimated recursively using an Extended Kalman Filter and can
be easily optimized using gradient-based methods to compute maximum likelihood
estimators. Our compartmental model is trained using GPS mobility data that
measures the mobility patterns of millions of mobile phones across the United
States. We show that, after calibrating against incidence and deaths data from
the city of Philadelphia, our model is able to produce an accurate 30-day
forecast of the evolution of the pandemic.
