1. Epidemiological parameters from transmission experiments: new methods for old data Simon Gubbins, David Schley & Ben Hu Transmission Biology Group The Pirbright Institute

2. Background
Transmission experiments are commonly used in foot-and-mouth disease research
They are used to estimate:
transmission rates
basic reproduction number (R0)
latent, infectious and incubation periods
vaccine effectiveness

3. Experimental design
Most transmission experiments follow a similar design ... C1
inoculate a number of donors C1 C2
introduce a number of naïve recipients C1 C2
observe the outcome: clinical
virological
immunological

4. Features of the experiments
We don’t directly observe what we’re interested in!
infection times
latent periods
infectious periods (typically rely on proxy measures)
Most commonly used methods for analysing transmission experiments (final size; generalized linear model) have to make assumptions to overcome these features

5. Bayesian methods: a better approach?
Using Bayesian methods allows us to avoid most assumptions
Allows us to draw inferences about unobserved processes (data augmentation):
infection times
latent and infectious periods
Allows us to incorporate data from previous experiments (priors)

6. Example 1: FMDV in lambs Follows the generic experimental design
parameter
previous
Bayes R0
1.14
(0.3, 3.3)
1.45
(0.33, 3.08)
mean latent period (days)
inoculated -
1.12
(0.68, 1.68)
contact
1.50
(0.16, 2.84)
mean infectious period (days)
21.1
(10.6, 42.1)
15.4
(11.0, 21.4)
Data from Orsel et al. (2007) Vaccine 25,

7. Example 2: FMDV in pigs Two experimental designs
results analysed together
Data from Orsel et al. (2007) Vaccine 25,

8. Example 2 (ctd): FMDV in pigs
parameter
previous
Bayes R0 ∞
8.54
(4.41, 14.9)
transmission rate
6.84
(3.17, 14.8)
1.51
(0.76, 2.55)
mean latent period (days)
inoculated -
0.97
(0.40, 1.67)
contact
0.14
(0.01, 0.33)
mean infectious period (days)
4.74
(3.83, 5.86)

9. Example 2 (ctd): FMDV in pigs
Vaccination significantly reduces R0, but not to below 1
previous analyses could not identify a significant effect of vaccination

10. When is an animal infectious?
This is critical to inferring transmission dynamics
Often inferred from proxy measures
detection of virus in blood, probang, nasal swabs ...
Can we infer infectiousness directly?
and, hence, identify a robust proxy measure

11. Experimental design Day 0 Day 2 Day 4 Day 6 Day 8
Virological data: blood, nasal swabs, probang
Clinical signs
Transmission
Data from Charleston et al. (2011) Science 332,

12. Quantifying infectiousness
We analyse the data assuming infectiousness changes continuously over time
cf. latent and infectious periods
The approach also
links infectiousness and onset of clinical signs
allows for individual variation in infectiousness
Implemented in a Bayesian framework

14. Does this matter?
Choice of proxy measure influences conclusions about:
basic reproduction number
generation time
effectiveness of reactive control measures
These effects scale up to the herd level

15. Conclusions
Bayesian methods facilitate analysis of transmission experiments
reduce the number of assumptions to be made
obtain estimates where classical methods fail
Generate insights into transmission processes
dynamics of infectiousness
who infects whom
Quantification of uncertainty in epidemiological parameters
essential when incorporating estimates in regional scale models of spread and control

16. Acknowledgements Everyone whose data we’ve stolen
José Gonzáles (WBR Lelystad)
Bryan Charleston (Pirbright)
Mark Woolhouse (Edinburgh)
Mike Tildesley (Warwick)
Leon Danon (Bristol)