### Bayesian uncertainty quantification for transmissibility of influenza, norovirus and Ebola using information geometry

Authors: Thomas House, Ashley Ford, Shiwei Lan, Samuel Bilson, Elizabeth Buckingham-Jeffery, Mark Girolami

Journal: Journal of the Royal Society Interface

Publication Date: 24 August, 2016

Department of: Mathematics

### In Abstract

##### In abstract:

**New insights into the dynamics of infectious disease**

When you become infectious, a period of time passes before you are able to infect others, and then once you are able to infect others, a period of time passes before you recover. In more technical language, the natural history of your infection can be modelled mathematically as passing at random times through a series of stages. In various experimental setups, individual cases have the amount of virus they have produced monitored over time since infection – however, determining the rates of transition between stages from these data is not straightforward.

Now, researchers from the Universities of Manchester, Warwick and Bristol have proposed a solution to this problem. They use a Bayesian approach to inference, coupled with ideas from information geometry, to determine the quantities of epidemiological interest. This yields new insight into the dynamics of two of the most prevalent human pathogens – influenza and norovirus – as well as Ebola virus disease.

- Riemannian Geometry was developed to study smooth, curved objects and it was traditionally used by theoretical physicists to model the universe. More recently it is applied to statistical inference.
- In a Bayesian approach, we consider which values of underlying physical / biological quantities are ‘credible’ given the data, which is a more sophisticated way of dealing with uncertainty in complex models than looking for which are ‘most likely’.
- Here we combine Reimannian geometry with Bayesian inference in the context of looking at data on individuals infected with different diseases to improve our understanding of what happens at the level of an individual case and how to propagate that forwards to make population-level predictions.