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.