Chronic Wasting Disease Research at
the USGS-Wisconsin Cooperative Wildlife Research Unit
Epizootiological Modeling

Models
are critical for the understanding and management of complex ecological systems
such as infectious diseases. Models help to define problems and assumptions,
they provide insights with respect to the structure and function (e.g.,
relationship and parameters) of the ecological system, they allow the
integration of knowledge from disparate sources and scales, extrapolate them in
space and time in order to produce predictions, and provide a framework for
evaluation of alternative management/conservation strategies.
In this study, we apply a top-down modeling strategy
in which we develop several model versions at increasing levels of complexity.
Currently we are developing a deterministic, non-spatial three-dimensional
population matrix model. The three dimensions are: age, sex, and infection
stage (Fig. 1). There are 20 semi-annual age classes (max age 10 yr.), and four
infection classes: susceptible (S), infectious (I) (infection only of lymph
nodes), mildly affected (M) (brain-stem infection), and clinical (C) in which
brain vacuolization is shows associated with behavioral changes and physical
emaciation. By six month a clinically ill animal is assumed to die. All deer
are assumed to be born susceptible. The model is season-specific with harvest
taking place in the winter time-step (October – March) and reproduction in the
summer time-step (April – September) All animals may, or may not, transition
between infection states at the probabilities described in Fig. 2. The
model is a composite matrix composed of age-dependent sub-matrices nested
within infection and sex classes, which calculate the transition probability
(Fig. 2).
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Fig.
1. Model structure: The three dimensions are – age, sex, and infection stage. Arrows
describe the different transitions implemented in the model. Left figure
depicts all the potential transitions for females only, and the right for both
sexes.

Fig. 2. Transition probabilities calculated for the model. Epidemiological
parameters are based on age-prevalence profiles (incidence rates) and disease
progression time line. Demographic parameters are based on estimates used by
the WDNR deer management models.
Model
confirmation and validation
To assess the model performance we compared its
predictions with empirical data with respect to the affect of deer harvest
rates on the deer population finite growth rate (Fig. 3) and age-prevalence
distribution (Fig. 4).

Fig.
3. The effect of harvest on deer population growth rate (l): simulated
vs. observed population dynamics

Fig.
4. Comparison of the observed and predicted prevalence-by-age distribution
given the estimated female and male specific incidence rates (bf) and (bm)
pre-CWD harvest rates.
In both cases we found a fairly good agreement
between the observed and expected patterns.
Preliminary
results
Given, initial, simplistic assumptions of constant
transmission rate and density independent harvest rate, we asked the following
three questions:
1. How might CWD affect deer population dynamics?
2. How might CWD affect deer harvest?
3. How might harvest, as a management tool, affect CWD?
Our
results suggest the following:
1. Assuming transmission rate increases with time since
its introduction, if not controlled, CWD, by increasing mortality, has a
potentially detrimental effect on deer population persistence.
2.
Given the same assumption, neglecting to control CWD might have dire
consequences to deer harvest.
3. Doe-biased harvest is more effective in reducing the
number of infectives through the reduction of the number of susceptibles. We
suggest that in addition increased buck harvest would also help to reduce the
number and distribution of the infection sources
Next
steps in model development: