Modeling of wildlife-associated zoonoses: applications and caveats

Abstract

Wildlife species are identified as an important source of emerging zoonotic disease. Accordingly, public health programs have attempted to expand in scope to include a greater focus on wildlife and its role in zoonotic disease outbreaks. Zoonotic disease transmission dynamics involving wildlife are complex and nonlinear, presenting a number of challenges. First, empirical characterization of wildlife host species and pathogen systems are often lacking, and insight into one system may have little application to another involving the same host species and pathogen. Pathogen transmission characterization is difficult due to the changing nature of population size and density associated with wildlife hosts. Infectious disease itself may influence wildlife population demographics through compensatory responses that may evolve, such as decreased age to reproduction. Furthermore, wildlife reservoir dynamics can be complex, involving various host species and populations that may vary in their contribution to pathogen transmission and persistence over space and time. Mathematical models can provide an important tool to engage these complex systems, and there is an urgent need for increased computational focus on the coupled dynamics that underlie pathogen spillover at the human-wildlife interface. Often, however, scientists conducting empirical studies on emerging zoonotic disease do not have the necessary skill base to choose, develop, and apply models to evaluate these complex systems. How do modeling frameworks differ and what considerations are important when applying modeling tools to the study of zoonotic disease? Using zoonotic disease examples, we provide an overview of several common approaches and general considerations important in the modeling of wildlife-associated zoonoses.

FIG. 1.

Anthrax is an obligate spillover pathogen for which cases are associated with direct interactions with the environment where the pathogen is sustained. Environmental and seasonal changes associated with bacterial storage areas are the primary drivers of epidemics, with human cases most likely directly linked to animal cases.

FIG. 2.

Ebola is an emerging zoonotic disease for which spillover dynamics appear to include up to four coupled systems. Population dynamics and seasonal influences appear to be the primary drivers of the process of pathogen invasion.

FIG. 3.

In the ecological niche modeling approach, environmental data and disease (pathogen, host, or vector) occurrence data are combined in a niche theory framework to model the multi-variate space where the species is likely to be present. This modeled relationship is then applied to the landscape pixel-by-pixel to identify all regions where the species may be present. Successful models of the species on the known geography can be projected onto novel landscapes or the known landscape in future time periods to evaluate unknown regions or climate-related changes in distribution (NDVI, Normalized Difference Vegetation Index).

FIG. 4.

In the compartmental approach, each entity or interaction in Ebola viral transmission must be partitioned into a compartment (S, susceptible; E, exposed; I, infectious; R, recovered). The combination of lines across all layers and compartments necessitates a single equation. Parameterizing and solving these equations becomes difficult, and therefore limits model resolution and complexity.

FIG. 5.

A compartmental model is often used when the average characteristic patterns of the population or group are equivalent to individual level attributes (A). However, when population level patterns are no longer equivalent to individual level detail, and it is the individual level characteristics that are needed to derive key aggregate population level patterns (B), an agent-based model (ABM) will increasingly be required. Thus the more individual characteristics deviate or are suspected to deviate from population level patterns, the more complex the modeling requirements become (arrow at right).

FIG. 6.

In the patch modeling approach, the environment is divided into patches to capture the heterogeneities from environmental factors. Within each patch a compartmental model, parameterized by these factors, is used to model the populations represented in this area. These compartmental models are also linked to adjacent patches to capture the population movements between the different patches (S, susceptible; E, exposed; I, infectious; R, recovered).

FIG. 7.

In an agent-based approach, individual behaviors and interactions can be represented across multiple coupled networks. These interactions can induce changes in the entities, which can, in turn, change which entities they interact with, and the nature of the interactions themselves.