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In this paper we introduce a novel description of the equilibrium state of abond percolation process on random graphs using the exact method of generatingfunctions. This allows us to find the expected size of the giant connectedcomponent (GCC) of two sequential bond percolation processes in which the bondoccupancy probability of the second process is modulated (increased ordecreased) by a node being inside or outside of the GCC created by the firstprocess. In the context of epidemic spreading this amounts to both aantagonistic partial immunity or a synergistic partial coinfection interactionbetween the two sequential diseases. We examine configuration model networkswith tunable clustering. We find that the emergent evolutionary behaviour ofthe second strain is highly dependent on the details of the coupling betweenthe strains. Contact clustering generally reduces the outbreak size of thesecond strain relative to unclustered topologies; however, positiveassortativity induced by clustered contacts inverts this conclusion for highlytransmissible disease dynamics.

Symbiotic and antagonistic disease dynamics on networks using bond percolatio