Epidemics on interconnected networks.

Populations are seldom completely isolated from their environment. Individuals in a particular geographic or social region may be considered a distinct network due to strong local ties but will also interact with individuals in other networks. We study the susceptible-infected-recovered process on interconnected network systems and find two distinct regimes. In strongly coupled network systems, epidemics occur simultaneously across the entire system at a critical infection strength ß(c), below which the disease does not spread. In contrast, in weakly coupled network systems, a mixed phase exists below ß(c) of the coupled network system, where an epidemic occurs in one network but does not spread to the coupled network. We derive an expression for the network and disease parameters that allow this mixed phase and verify it numerically. Public health implications of communities comprising these two classes of network systems are also mentioned.

Critical behavior and Griffiths effects in the disordered contact process.

We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte Carlo simulations for times up to 10(9) and system sizes up to 10(7) sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of 10(4) or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder.