Bifurcations in synergistic epidemics on random regular graphs

The role of cooperative effects (i.e. synergy) in transmission of infection is investigated analytically and numerically for epidemics following the rules of susceptible-infected-susceptible (SIS) model defined on random regular graphs. Non-linear dynamics are shown to lead to bifurcation diagrams for such spreading phenomena exhibiting three distinct regimes: non-active, active and bi-stable. The dependence of bifurcation loci on node degree is studied and interesting effects are found that contrast with the behaviour expected for non-synergistic epidemics.FJPR acknowledges financial support from the Carnegie Trust

A single-walker approach for studying quasi-nonergodic systems

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-nonergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.The work has been supported by a grant from EPSRC

Understanding disease control: influence of epidemiological and economic factors

We present a local spread model of disease transmission on a regular network and compare different control options ranging from treating the whole population to local control in a well-defined neighborhood of an infectious individual. Comparison is based on a total cost of epidemic, including cost of palliative treatment of ill individuals and preventive cost aimed at vaccination or culling of susceptible individuals. Disease is characterized by pre- symptomatic phase which makes detection and control difficult. Three general strategies emerge, global preventive treatment, local treatment within a neighborhood of certain size and only palliative treatment with no prevention. The choice between the strategies depends on relative costs of palliative and preventive treatment. The details of the local strategy and in particular the size of the optimal treatment neighborhood weakly depends on disease infectivity but strongly depends on other epidemiological factors. The required extend of prevention is proportional to the size of the infection neighborhood, but this relationship depends on time till detection and time till treatment in a non-nonlinear (power) law. In addition, we show that the optimal size of control neighborhood is highly sensitive to the relative cost, particularly for inefficient detection and control application. These results have important consequences for design of prevention strategies aiming at emerging diseases for which parameters are not known in advance

On the origin of the Boson peak in globular proteins

We study the Boson Peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean Random Matrix theory, whose predictions can be numerically tested on real proteins structures. We find that the emergence of the Boson Peak is strictly related to an intrinsic mechanical instability of the protein, in close similarity to what is thought to happen in glasses. The biological implications of this conclusion are also discussed by focusing on a representative case study.Comment: Proceedings of the X International Workshop on Disordered Systems, Molveno (2006

Explosive Contagion in Networks.

The spread of social phenomena such as behaviors, ideas or products is an ubiquitous but remarkably complex phenomenon. A successful avenue to study the spread of social phenomena relies on epidemic models by establishing analogies between the transmission of social phenomena and infectious diseases. Such models typically assume simple social interactions restricted to pairs of individuals; effects of the context are often neglected. Here we show that local synergistic effects associated with acquaintances of pairs of individuals can have striking consequences on the spread of social phenomena at large scales. The most interesting predictions are found for a scenario in which the contagion ability of a spreader decreases with the number of ignorant individuals surrounding the target ignorant. This mechanism mimics ubiquitous situations in which the willingness of individuals to adopt a new product depends not only on the intrinsic value of the product but also on whether his acquaintances will adopt this product or not. In these situations, we show that the typically smooth (second order) transitions towards large social contagion become explosive (first order). The proposed synergistic mechanisms therefore explain why ideas, rumours or products can suddenly and sometimes unexpectedly catch on