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.