Percolation models of pathogen spillover

A series of logical events must occur for a pathogen to spill over from animals to people. The pathogen must be present in an animal reservoir, it must be shed from the reservoir into the environment or be transferred from the reservoir to a vector, it must persist in the environment or vector until contact with a human or amplifier host, and it must successfully enter, colonize, and reproduce within the human. These events each represent a barrier the pathogen must cross to successfully infect a human. Percolation models of pathogens completing the series of barriers or logical events can connect models of spillover risk with standard tools for statistical inference. Here, we develop percolation-based models of spillover risk and a theoretical framework for managing spillover as an inextricably multilevel process. Through analysis and simulation, we show that estimated associations between level-specific covariates and spillover events will err towards associations from dominant pathway to spillover, a potential problem if there are alternative pathways to spillover with different associations with covariates. Furthermore, estimated associations between covariates and spillover will better reflect associations between covariates and success probabilities of bottleneck events with the highest pathogen attrition rates in the data observed. If one agrees with a percolation model for spillover, then GLMs should not be used to estimate relative importance of various levels. We recommend always using nonlinear models for predicting spillover risk with quantitative covariates and discuss why switching regression models may be well suited for avoiding some obvious pitfalls in predicting spillover from alternative pathways or wildlife reservoirs. Finally, we demonstrate how percolation models formalize an intuitive management paradigm for mitigating risk in the inherently multilevel process of pathogen spillover.