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).

 

 

 

 

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:

 

 

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