Simplifying networks: Spread of White-nose syndrome in North America

Background/Question/Methods

Network models can be used to understand and predict the patterns of spread that occur during disease emergence or species invasions. These models are often biologically realistic in representing spread as taking place between discrete patches or individuals. They also can be computationally intensive and difficult to translate into applications, such as designing control efforts, due to their complexity. This is especially true for fully connected networks where spread can theoretically occur between any two nodes in a single step. We have previously developed a model for county-scale spread of White-nose syndrome (WNS), a deadly fungal infection of cave-dwelling bats in North America. Given the paucity of information on spread mechanisms, fitting the model to infection data on the fully connected network avoided imposing apriori structure. The downside was a directional, weighted network with >10⁶ edges. Our approach to simplifying the network was to iteratively remove edges with the lowest infection probabilities and then refit model parameters. We removed edges until the model became statistically distinguishable from the fully connected network as signified by ΔAIC>2 or until the model could no longer be estimated. Three algorithms for edge removal were compared to examine the balance of optimality and computational efficiency.

Results/Conclusions

We found that 77% of network edges could be removed before model fit deteriorated past our cutoff. Parameter estimates for the effects of distance, cave density, and winter length on probability of WNS infection were identical to 2 decimal places between the full and simplified networks. Our most efficient algorithm for network simplification was indistinguishable from the optimal approach of removing one edge at a time that took ~700 times more computational effort. The average unweighted degree of nodes (counties) in the simplified network was one-half of the full network (524 to 1133) while the average weighted degree was unchanged (0.84). Diameter and average betweenness increased in the simplified network while algebraic connectivity, a measure of overall network connectivity, declined (1134 to 1). We have demonstrated that this model of WNS dynamics can be substantially simplified while maintaining spread characteristics and explanatory power of the best-fit model on the full network. The simplified network offers distinct advantages for visualization and use in other computational extensions such as assessing control options for this important threat to bat populations. This approach to network simplification is applicable to other situations where spread over time has been fit with a network model.