# Epidemic inverse problems: geometry and sampling

Lead Research Organisation: University of Warwick
Department Name: Mathematics

### Abstract

Imagine an epidemic is doubling in size every six days soon after the first
cases are announced. If you know cases are all infectious for six days then a
back-of-the envelope calculation tells you that each case infects on average a
further three before recovering and vaccine coverage of 67% or greater is
needed to contain the outbreak. But if you don't know anything about how long
people with the disease are contagious for, then this simple calculation cannot

This project aims to quantify that uncertainty, so that when a measurement of
the duration of infectiousness is made then we will be able to assess how
infectious the disease associated with a particular outbreak is likely to be.

Also, when you have a cold then it is is convenient to describe your disease
state 'categorically', which is to say that you will say "I'm coming down with
a cold", "I'm in the middle of a cold", or "I'm just getting better from a
cold", rather than "my viral titre is probably 3 on a logarithmic scale". It
is also often convenient for scientific epidemiologists to take a categorical
approach to disease state, and this project proposes to find a reliable method
for deciding what the relevant categories should be.

### Planned Impact

The following non-academics have been identified as benificiaries of the
research:

1. The public through enhanced understanding of infectious disease
epidemiology;
2. Non-academic biostatisticians and epidemiologists who will be able to use
the methods developed.

### Publications

10 25 50

Description 1) That we have better models for understanding the dynamics of an epidemic which can use data which repeatedly samples who is shedding virus, in particular influenza (via nasal swab), norovirus (via stool sample) and ebola (via blood titre). Previously analysing this data using our standard models was challenging, and more complex models are less amenable to analysis. In this project we have developed methods to fit standard models using this type of data.

(2) That we have better methods for large-scale multiple imputation to inform epidemiological models. This was a particularly challenging, as it is difficult to weight the different data sources correctly, but we have overcome this by developing new methodologies.
Exploitation Route This grant has developed two types of findings which can be brought forward. The analysis of respiratory syncytial virus will be used to inform control policy for this potentially deadly disease. In addition, the novel methodologies for analysing the data will inform both other modelling studies and epidemiological study design.
Sectors Healthcare