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Register a new userFirst-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process
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In co-infections, positive feedback between multiple diseases can accelerate outbreaks. In a recent letter Chen, Ghanbarnejad, Cai, and Grassberger (CGCG) introduced a spatially homogeneous mean-field model system for such co-infections, and studied this system numerically with focus on the possible existence of discontinuous phase transitions. We show that their model coincides in mean-field theory with the homogenous limit of the extended general epidemic process (EGEP). Studying the latter analytically, we argue that the discontinuous transition observed by CGCG is basically a spinodal phase transition and not a first-order transition with phase-coexistence. We derive the conditions for this spinodal transition along with predictions for important quantities such as the magnitude of the discontinuity. We also shed light on a true first-order transition with phase-coexistence by discussing the EGEP with spatial inhomogeneities.
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Background: The global spread of the severe acute respiratory syndrome (SARS) epidemic has clearly shown the importance of considering the long-range transportation networks in the understanding of emerging diseases outbreaks. The introduction of extensive transportation data sets is therefore an important step in order to develop epidemic models endowed with realism. Methods: We develop a general stochastic meta-population model that incorporates actual travel and census data among 3 100 urban areas in 220 countries. The model allows probabilistic predictions on the likelihood of country outbreaks and their magnitude. The level of predictability offered by the model can be quantitatively analyzed and related to the appearance of robust epidemic pathways that represent the most probable routes for the spread of the disease. Results: In order to assess the predictive power of the model, the case study of the global spread of SARS is considered. The disease parameter values and initial conditions used in the model are evaluated from empirical data for Hong Kong. The outbreak likelihood for specific countries is evaluated along with the emerging epidemic pathways. Simulation results are in agreement with the empirical data of the SARS worldwide epidemic. Conclusions: The presented computational approach shows that the integration of long-range mobility and demographic data provides epidemic models with a predictive power that can be consistently tested and theoretically motivated. This computational strategy can be therefore considered as a general tool in the analysis and forecast of the global spreading of emerging diseases and in the definition of containment policies aimed at reducing the effects of potentially catastrophic outbreaks.
We study epidemic outbreaks on random Delaunay triangulations by applying Asynchronous SIR (susceptible-infected-removed) model kinetic Monte Carlo dynamics coupled to lattices extracted from the triangulations. In order to investigate the critical behavior of the model, we obtain the cluster size distribution by using Newman-Ziff algorithm, allowing to simulate random inhomogeneous lattices and measure any desired percolation observable. We numerically calculate the order parameter, defined as the wrapping cluster density, the mean cluster size, and Binder cumulant ratio defined for percolation in order to estimate the epidemic threshold. Our findings suggest that the system falls into two-dimensional dynamic percolation universality class and the quenched random disorder is irrelevant, in agreement with results for classical percolation.
A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal first-order transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient.
In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time, which fundamentally influences the dynamics of spreading processes on them and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously in time. In our work, we encode the continuous time-dependence of networks into the evaluation of the epidemic threshold of a susceptible--infected--susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors---the decay coefficients of the tie strengths in a network, the frequency of interactions between nodes, and the sparsity of the underlying social network in which interactions occur---lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.
The present paper considers some classical ferromagnetic lattice--gas models, consisting of particles that carry $n$--component spins ($n=2,3$) and associated with a $D$--dimensional lattice ($D=2,3$); each site can host one particle at most, thus implicitly allowing for hard--core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic, and site occupation is also controlled by the chemical potential $mu$. The models had previously been investigated by Mean Field and Two--Site Cluster treatments (when D=3), as well as Grand--Canonical Monte Carlo simulation in the case $mu=0$, for both D=2 and D=3; the obtained results showed the same kind of critical behaviour as the one known for their saturated lattice counterparts, corresponding to one particle per site. Here we addressed by Grand--Canonical Monte Carlo simulation the case where the chemical potential is negative and sufficiently large in magnitude; the value $mu=-D/2$ was chosen for each of the four previously investigated counterparts, together with $mu=-3D/4$ in an additional instance. We mostly found evidence of first order transitions, both for D=2 and D=3, and quantitatively characterized their behaviour. Comparisons are also made with recent experimental results.
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