SCientifiC REPORtS | 7: 16774 | DOI:10.1038/s41598-017-17174-8
Bayesian inference of
epidemiological parameters from
, Jose L. Gonzales
& Simon Gubbins
Epidemiological parameters for livestock diseases are often inferred from transmission experiments.
However, there are several limitations inherent to the design of such experiments that limits the
precision of parameter estimates. In particular, infection times and latent periods cannot be directly
observed and infectious periods may also be censored. We present a Bayesian framework accounting
for these features directly and employ Markov chain Monte Carlo techniques to provide robust
inferences and quantify the uncertainty in our estimates. We describe the transmission dynamics using
a susceptible-exposed-infectious-removed compartmental model, with gamma-distributed transition
times. We then t the model to published data from transmission experiments for foot-and-mouth
disease virus (FMDV) and African swine fever virus (ASFV). Where the previous analyses of these data
made various assumptions on the unobserved processes in order to draw inferences, our Bayesian
approach includes the unobserved infection times and latent periods and quanties them along with
all other model parameters. Drawing inferences about infection times helps identify who infected
whom and can also provide insights into transmission mechanisms. Furthermore, we are able to use
our models to measure the dierence between the latent periods of inoculated and contact-challenged
animals and to quantify the eect vaccination has on transmission.
Transmission experiments oer a wealth of data from which we can estimate important epidemiological parame-
ters for livestock diseases. e basic reproduction number (R
), dened as the average number of secondary cases
caused by an infected individual in a totally susceptible population
, transmission rates and latent and infectious
period durations can all be inferred from such experiments. is is particularly important for high consequence
animal diseases, such as avian inuenza, foot-and-mouth disease, African swine fever or classical swine fever.
For these diseases, collecting data during outbreaks is oen hampered by a lack of capacity in parts of the world
where they are endemic and by a conict between the requirements for expeditious disease control versus infor-
mation gathering when epidemics occur in disease-free countries. Consequently, transmission experiments are
oen the primary source of data from which to infer transmission, latent period or infectious period parameters.
Estimating these parameters directly from the data, rather than making simplifying assumptions or relying on
, lends good strength to any conclusions drawn.
Many transmission experiments follow a similar design in which the pathogen of interest is introduced to a
group of animals, usually by some inoculated seed animals, and the subsequent spread through the rest of the
population is recorded
. Generally, all individuals are monitored for clinical signs and biological samples are
collected at regular intervals to detect the pathogen (i.e. to determine whether or not transmission has occurred).
However, this design means that the latent periods for the inoculated animals are only known in the range
between the last negative and rst positive samples. More importantly, the infection times and latent periods
of the in-contact animals are unobserved. Finally, the infectious periods are similarly unobserved and may also
be right-censored due to the pre-determined experiment duration
or welfare grounds, in the case of severe
. In addition, the test used to detect the pathogen is assumed to be perfect, so that the test results provide
an accurate picture of if and when an animal is infected. e numbers of animals that can be used in this type
of experiment are also limited on logistical (numbers of animals that can be housed), cost (experiments in high
containment are expensive) and ethical (with the aim of reducing the number of animals used in experiments)
The Pirbright Institute, Ash Road, Pirbright, Surrey, GU24 0NF, UK.
Centre for Complexity Science, University of
Warwick, Coventry, CV4 7AL, UK.
Wageningen BioVeterinary Research, Houtribweg 39, 8221 RA, Lelystad, The
Netherlands. Correspondence and requests for materials should be addressed to S.G. (email: simon.gubbins@
Received: 23 May 2017
Accepted: 21 November 2017
Published: xx xx xxxx