1.
European Commission for the Control
of Foot-and-Mouth Disease
Open Session of the EuFMD - Cascais –Portugal 26-28
October 2016
Epidemiological parameters from
transmission experiments: new methods
for old data
Simon Gubbins, David Schley & Ben Hu
Transmission Biology Group
The Pirbright Institute

2.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
Experimental design
• Most transmission experiments follow a similar design ...
C1
C1
inoculate a number
of donors
C1
C1
C2
C2
introduce a
number of naïve
recipients
C1
C1
C2
C2
observe the outcome:
clinical
virological
immunological

4.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
Example 1: FMDV in lambs
• Follows the generic experimental design
Data from Orsel et al. (2007) Vaccine 25, 2673-2679
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)

7.
European Commission for the Control
of Foot-and-Mouth Disease
Example 2: FMDV in pigs
• Two experimental designs
– results analysed together
Data from Orsel et al. (2007) Vaccine 25, 6381-6391

8.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
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, 726-729

12.
European Commission for the Control
of Foot-and-Mouth Disease
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

13.
European Commission for the Control
of Foot-and-Mouth Disease

14.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
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.
European Commission for the Control
of Foot-and-Mouth Disease
Acknowledgements
• Everyone whose data we’ve stolen
• José Gonzáles (WBR Lelystad)
• Bryan Charleston (Pirbright)
• Mark Woolhouse (Edinburgh)
• Mike Tildesley (Warwick)
• Leon Danon (Bristol)