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There are two standard "Ising" models for the spreading of epidemics, the "SIS" (susceptible-infected-susceptible) epidemic and the "SIR" (susceptible-infected-removed) model. Both are related to percolation - the first to directed, the second to undirected - and thus both show continuous ("second-order") phase transitions when the conditions for spreading are critical. Recently, much interest has been roused by models which show first order transitions. After giving a short overview I will concentrate on first order transitions in models with cooperativity. This cooperativity can be of two very different types. On the one hand, several agents on neighboring nodes in a network (or sites on a lattice) can cooperate in infecting a new node (like three friends who convince you more easily than any single one of them to adopt a political opinion). On the other hand, also two pathogens (like HIV and TB) can cooperate in the sense that one of them lowers the resistance to the other. In the first case the transition from a continuous to a discontinuous phase transition is a standard tricritical point (with higher n-point interactions in a field theoretic formalism), while in the second one one has a multi-component order parameter. In several instances, the resulting first order transitions are actually "hybrid", i.e. they involve also features of second-order transitions like scaling. In one case, one even finds that two order parameter definitions which coincide for ordinary percolation display different transition orders.

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Prof. Dr. Peter Grassberger, Jülich Supercomputing Centre
Seminarraum Theoretische Physik
Contact: Joachim Krug