Control and surveillance of partially observed stochastic epidemics in a Bayesian framework
Abstract
This thesis comprises a number of inter-related parts. For most of the thesis we are
concerned with developing a new statistical technique that can enable the identi cation
of the optimal control by comparing competing control strategies for stochastic
epidemic models in real time. In the second part, we develop a novel approach for
modelling the spread of Peste des Petits Ruminants (PPR) virus within a given country
and the risk of introduction to other countries.
The control of highly infectious diseases of agriculture crops, animal and human
diseases is considered as one of the key challenges in epidemiological and ecological
modelling. Previous methods for analysis of epidemics, in which different controls
are compared, do not make full use of the trajectory of the epidemic. Most methods
use the information provided by the model parameters which may consider partial
information on the epidemic trajectory, so for example the same control strategy
may lead to different outcomes when the experiment is repeated. Also, by using
partial information it is observed that it might need more simulated realisations when
comparing two different controls. We introduce a statistical technique that makes full
use of the available information in estimating the effect of competing control strategies
on real-time epidemic outbreaks. The key to this approach lies in identifying a suitable
mechanism to couple epidemics, which could be unaffected by controls. To that end,
we use the Sellke construction as a latent process to link epidemics with different
control strategies.
The method is initially applied on non-spatial processes including SIR and SIS
models assuming that there are no observation data available before moving on to
more complex models that explicitly represent the spatial nature of the epidemic
spread. In the latter case, the analysis is conditioned on some observed data and
inference on the model parameters is performed in Bayesian framework using the
Markov Chain Monte Carlo (MCMC) techniques coupled with the data augmentation
methods. The methodology is applied on various simulated data sets and to citrus
canker data from Florida. Results suggest that the approach leads to highly positively
correlated outcomes of different controls, thus reducing the variability between the
effect of different control strategies, hence providing a more efficient estimator of their
expected differences. Therefore, a reduction of the number of realisations required to compare competing strategies in term of their expected outcomes is obtained.
The main purpose of the final part of this thesis is to develop a novel approach
to modelling the speed of Pest des Petits Ruminants (PPR) within a given country
and to understand the risk of subsequent spread to other countries. We are interested
in constructing models that can be fitted using information on the occurrence
of outbreaks as the information on the susceptible population is not available, and use
these models to estimate the speed of spatial spread of the virus. However, there was
little prior modelling on which the models developed here could be built. We start
by first establishing a spatio-temporal stochastic formulation for the spread of PPR.
This modelling is then used to estimate spatial transmission and speed of spread. To
account for uncertainty on the lack of information on the susceptible population, we
apply ideas from Bayesian modelling and data augmentation by treating the transmission
network as a missing quantity. Lastly, we establish a network model to address
questions regarding the risk of spread in the large-scale network of countries and
introduce the notion of ` first-passage time' using techniques from graph theory and
operational research such as the Bellman-Ford algorithm. The methodology is first
applied to PPR data from Tunisia and on simulated data. We also use simulated
models to investigate the dynamics of spread through a network of countries.