A Time-Stepper Neural Network Model for the Maximum Likelihood Estimation of Epidemic Parameters

Inference for dynamical systems and their relevant physical parameters provide us with important insights that aid decision-making, especially in the case of epidemics. In recent years, there has been growing interest in utilizing artificial neural network models to approximate or solve dynamical system trajectories, due to their universal approximation capabilities and availability of various architectures that provide a large range of flexibility during training. This article explores time-stepper neural network models which approximate the evolution of epidemic compartments (susceptibles, infectious and removed) between subsequent time points, within a specified range of parameter settings. The resulting approximation is then applied to a maximum likelihood estimation algorithm to estimate epidemic parameters such as the contact rates and infectious rates. Crucially, the analytical tractability of the neural network model allows convenient uncertainty quantifications of such parameter estimates. We examine the accuracy of this model in comparison to high-accuracy numerical integration methods as benchmark, and discuss its advantages and limitations.