Introduction
Host-pathogen systems are characterised by the complex networks of
interactions between an infectious agent and its host species . Examples
of such host-pathogen systems are bovine tuberculosis (bTB) , Severe
Acute Respiratory Syndrome coronavirus (SARS-CoV) or the
yet-unidentified wildlife host of SARS-CoV-2—the causative agent of
COVID-19. Given the severity and economic impact of these and similar
diseases, improved host-pathogen modelling capabilities will be of
undoubted value to epidemiologists and ecologists working towards
effective disease controls.
In comparison to their human counterparts, wildlife disease models
contend with a data-poor environment. Animals tend to be hard to track
and or trap, and infection-states can be hard to infer due to poor
quality diagnostic tests. Accordingly, a common purpose of wildlife
disease models is to describe known—or uncover unknown—latent
relationships between the identified factors that make up a disease
system, to better understand how disease spreads. Our synthesis is
restricted to statistical rather than analytical models of disease
processes because the parameters that may describe these processes vary
stochastically, as well as in time and space; and are rarely, if ever,
known .
Studying disease at a systems scale involves recognising the hierarchy
of interacting levels over which disease dynamics persist—termed in
this review as the ecological hierarchy (Figure 1) — and requires the
adoption of hierarchical models. Hierarchical models start from the
premise that a hierarchy of scale exists across ecological systems , and
explore the nested relationships between differently scaled variables
through sub-models, which link together to form a full model. For
example, major progress in eliminating the Sarcoptes scabiei mite
from bare-nosed wombat populations was facilitated by considering the
disease statuses of wombat burrows at the metapopulation level as well
as of the individual wombats; and consequently, both the burrowsand the wombats were modelled as hosts . Hierarchical modelling
has also enabled a database of bat hibernation roost surveys to be
analysed across time, space, and five species, to determine the latent
disease severity of Pseudogymnoascus destructans infections—the
causative agent of white-nose syndrome—at species and regional scales
in North America .
We also draw attention to a second type of hierarchy typical of data
associated with wildlife: the statistical hierarchy (Table 1). This
hierarchy also exists across ecological levels and scales, and
represents the hidden network of latent variables we wish to
infer—such as being infected or being dead —that can only be
measured by proxy, for instance, by live trapping, or by analysing the
results of imperfect diagnostic tests. The statistical hierarchy is
therefore a state-space representation of parameters that, when
inferred, will help us to understand wildlife disease either directly or
indirectly. We suggest that a “whole-system” approach to studying
wildlife disease is essential because most mechanisms of wildlife
disease transmission covary with other ecological parameters, are not
fully understood, and are impossible to measure directly. For example,
identifies substantial gaps in our knowledge of Chronic Wasting Disease
(CWD) ecology, such as its unidentified reservoir species, and the
biogeography of CWD transmission: a whole-system approach would be
directly applicable to this problem.
Parameterising the double-hierarchy of whole-system disease models
(ecological and statistical) is beyond the toolbox of classical,
frequentist or maximum likelihood statistical techniques. For systems in
which complexities prevent the definition of likelihood functions for
observed data, analysts might look to Approximate Bayesian Computation
or machine learning techniques to guide understanding of the system.
Here, though, we examine how Bayesian inference is under-utilised in
disease ecology yet is a powerful tool capable of quantifying unknown
and or unobserved latent variables within ecological networks, by
treating them as random variables described by probability distributions
. Disease status and mortality status are latent variables largely
unique to wildlife host-pathogen systems, and therefore are the
variables we draw particular attention to throughout this review.
Improving the capability of statistical models to describe entire
ecological systems is an important and desired advance in disease
ecology, particularly since understanding wildlife health is critical to
its management . Bayesian modelling is a pivotal and statistically
rigorous approach with which to improve both the parameterisation of
infectious disease processes , and learn the strength of whole-system
drivers such as disease incidence. Noticeably, the application of
Bayesian inference to disease modelling has been propelled by research
relating to the current COVID-19 pandemic . In this synthesis, we refer
to a whole-system model as one able to describe as many aspects of an
ecological network as possible, across a hierarchy of ecological scales
(Fig. 1).
We describe how Bayesian methods can help ecologists move towards a
whole-system approach to studying disease networks. Our recommendations
are unlikely to surprise statistical epidemiologists, but our finding is
that Bayesian methods remain under-used in wildlife disease research.
The review is structured sequentially as follows: first, we examine why
Bayesian inference should be used to model wildlife disease; second, we
show how Bayesian modelling has informed research into wildlife
reservoirs of bTB; third, we discuss why Bayesian hierarchical modelling
is essential to a whole-system approach; and finally, we clarify the
importance of latent variables and individual heterogeneities to a
whole-system model of wildlife disease. In these latter sections, we
include a survey of the literature to reveal that Bayesian approaches to
the modelling of wildlife disease are (a) relatively scarce and (b) tend
to infer only limited subsets of a whole-system model.