Epidemic inverse problems: geometry and sampling

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
be made without additional information.

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.

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.