Fig. 1.

Schematic representation of PKD transmission dynamics. a Within-season dynamics. The red-shaded area highlights the bryozoan sub-model. The circular arrows illustrate bryozoan growth. The dotted line indicates that the growth of overtly infected bryozoans is impaired by the parasite. The blue-shaded area highlights the fish sub-model. The dead-end arrow refers to excess PKD-induced fish mortality. In both sub-models, straight solid lines indicate fluxes among epidemiological classes, dashed arrows represent disease transmission between the two sub-systems. Natural mortality is not displayed. Parameters driving the transition between classes are displayed in gray. Letters T and τ indicate fluxes that are expected to be dependent on water temperature T and time τ. b Schematic representation of between-season (overwintering) dynamics relevant to PKD transmission. Colors as in (a). Continuous lines represent survival over winter. Dashed-dotted lines stand for reproduction processes. c Graphic timeline of the discrete-continuous hybrid model