Uncertainty Informed Optimal Resource Allocation with Gaussian Process
  based Bayesian Inference
Samarth Gupta Saurabh Amin
We focus on the problem of uncertainty informed allocation of medical
resources (vaccines) to heterogeneous populations for managing epidemic spread.
We tackle two related questions: (1) For a compartmental ordinary differential
equation (ODE) model of epidemic spread, how can we estimate and integrate
parameter uncertainty into resource allocation decisions? (2) How can we
computationally handle both nonlinear ODE constraints and parameter
uncertainties for a generic stochastic optimization problem for resource
allocation? To the best of our knowledge current literature does not fully
resolve these questions. Here, we develop a data-driven approach to represent
parameter uncertainty accurately and tractably in a novel stochastic
optimization problem formulation. We first generate a tractable scenario set by
estimating the distribution on ODE model parameters using Bayesian inference
with Gaussian processes. Next, we develop a parallelized solution algorithm
that accounts for scenario-dependent nonlinear ODE constraints. Our
scenario-set generation procedure and solution approach are flexible in that
they can handle any compartmental epidemiological ODE model. Our computational
experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate
that accounting for uncertainty in key epidemiological parameters can improve
the efficacy of time-critical allocation decisions by 4-8%. This improvement
can be attributed to data-driven and optimal (strategic) nature of vaccine
allocations, especially in the early stages of the epidemic when the allocation
strategy can crucially impact the long-term trajectory of the disease.