Abstract

The pandemic of the novel coronavirus, COVID -19, has hugely affected billions of people worldwide. Forecasting the course of an epidemic based on limited case data, when viewed as a problem of Bayesian inference, is beset by uncertainties in both the epidemiological model and its parameters. We assess the effect of these uncertainties for a family of age-structured compartment models. By formulating these models in terms of a chemical Master equation and taking a diffusion limit, we readily obtain a quasi-analytical expression for the parameter posterior distribution in the tangent space to the epidemiological solution manifold. The traceable form of the posterior distribution enables us to compute the Hessian matrix by automatic differentiation. Therefore, we can quantify the uncertainty of our parameter estimates exactly, and obtain a Laplacian approximation to the Bayesian model evidence.