Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks

Mathematical models in epidemiology strive to describe the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. Since high-fidelity models are often quite complex and analytically intractable, their applicability to real data depends on powerful estimation algorithms. Moreover, uncertainty quantification in such models is far from trivial, and different types of uncertainty are often confounded. With this work, we introduce a novel coupling between epidemiological models and specialized neural network architectures. This coupling results in a powerful Bayesian inference framework capable of principled uncertainty quantification and efficient amortized inference once the networks have been trained on simulations from an arbitrarily complex model. We illustrate the utility of our framework by applying it to real Covid-19 cases from entire Germany and German federal states.