Discontinuous phase transition via cooperation of spreading agents: How two evils are worse than one

Spreading of infective agents like pathogens, computer viruses, fashions, or political opinions can exhibit a percolation transition that separates small outbreaks from giant ones which reach a non-zero fraction of the population. Typically, such transitions are continuous (“second order”), but recently possible discontinuous (“first order”) transitions (DTs) have aroused huge interest. Here we present a model involving cooperativity between two different types of spreading agents: the presence of one facilitates the spreading of the other, and vice versa. We show that this mechanism can lead to DTs or to continuous ones, depending on the chosen order parameter, the topology of the underlying network, and on seemingly minor details of the implementation. Moreover, all DTs are also accompanied by various non-trivial power laws, which blurs the fundamental distinction between first and second order transitions.