Distinguishing between indirect and direct modes of transmission using epidemiological time series.

Pathogen transmission can involve direct and/or indirect pathways. Using theoretical models, in this study we ask, "do directly and indirectly transmitted pathogens yield different population-level epidemiological dynamics?" and "can the transmission pathway be inferred from population-level epidemiological data?" Our approach involves comparing the continuous-time dynamics of a class of compartmental epidemiological models with direct versus environmentally mediated indirect transmission pathways. Combing analytical theory and numerical simulations we show that models with direct and indirect transmission can produce quantitatively similar time series when the pathogen cannot reproduce in the environment, particularly when the environmental pathogen dynamics are fast. We apply these results to a previous study on chronic wasting disease and show that identifying the transmission pathway is more difficult than previously acknowledged. Our analysis and simulations also yield conditions under which numerical differences can potentially identify the transmission route in oscillating endemic systems and systems where the environmental pathogen dynamics are not fast. This work begins to identify how differences in the transmission pathway can result in quantitatively different epidemiological dynamics and how those differences can be used to identify the transmission pathway from population level time series.