Including individual heterogeneities is essential, but
difficult.
Studying disease on the individual level is difficult because single
transmission events are not just impossible to observe in the wild, but
also associated with a wide variety of host characteristics, such as
behaviour, antibodies, age, or senescence: measuring the relevant
predictors can be challenging. As explained above, there are few
examples of how individual states have been modelled using Bayesian
hierarchical models, including state-space techniques.
Wildlife diseases are often studied using data on antibodies or general
pathological observations . Consequently, many epidemiological
state-space models are based on serology records . Although the
seropositive statuses of most wild host species are unknown , it is
becoming increasingly important to look at the information that serology
records provide, to reveal individual heterogeneities. For example, inEidolon helvum fruit bats, seropositive thresholds were used to
distinguish between the genetic and acquired immunities to Lagos bat
virus and African henipavirus, using Bayesian mixture-models . Here,
Bayesian inference determined that immunity relied on patterns in
disease transmission , suggesting that serological data is an invaluable
way to measure individual heterogeneities. In turn, this suggests that
estimating seroprevalence is a good proxy for inferring the probability
of infection in the absence of reliable testing. Yet even though the
state-space models described in Table 3 are based on individual-level
data, the outcome is still on a population level, with highly
generalised disease processes , illustrating the difficulty in
disaggregating the individualistic characteristics of disease processes.
A further difficultly in representing the individual state within
state-space models is the complexity of the data involved. For wildlife
systems, ageing is a latent individual process with a limited
understanding particularly in terms of its relationship with disease.
Serological data has been directly associated with age to infer
infection rate, the probability of antibody loss and recovery rates in
brucellosis-infected Elk . Yet to infer these parameters, the authors
adopted Approximate Bayesian Computation methods due to the difficulty
in writing closed form likelihood functions for the study parameters,
and the associated difficulty in implementing them within a standard
Monte-Carlo Markov Chain algorithm . This is an example of where the
usefulness of Bayesian state-space modelling is currently limited in
terms of its accessibility to disease ecologists. Although it is likely
that the latent parameter “ageing” is intrinsically linked to disease
via a host of known and unknown latent variables: within the
whole-system model, this additional complexity must also be accounted
for. Bayesian methods are a practical tool of choice for modelling
complex systems, but realistically, the modelling of whole-systems using
the Bayesian hierarchical approaches described within this review will
rely on stronger collaborations between statisticians, epidemiologists
and ecologists.