Spreading with immunization in high dimensions

  title={Spreading with immunization in high dimensions},
  author={Stephan M. Dammer and Haye Hinrichsen},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  • S. DammerH. Hinrichsen
  • Published 25 May 2004
  • Mathematics
  • Journal of Statistical Mechanics: Theory and Experiment
We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, p0, and for reinfections, p. When the two probabilities are equal, the model reduces to directed percolation, while for perfect immunization one obtains the general epidemic process belonging to the universality class of dynamical percolation. We focus on the critical behaviour in the vicinity of the directed percolation point, especially for high number… 

Figures from this paper

Directed percolation with incubation times.

It is argued that the best approach to find the effective action for directed percolation is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice.

Critical behavior of the susceptible-infected-recovered model on a square lattice.

  • T. ToméR. Ziff
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
The critical behavior of the stochastic asynchronous susceptible-infected-recovered model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamicPercolation cluster growth, as is demonstrated explicitly.

A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold

A rigorous analysis of a model of reinfections shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described, and it is demonstrated that this threshold is the mean field version of a transition in corresponding spatial models of immunization.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible–infected–recovered model

The critical behavior of the stochastic susceptible–infected–recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the

Probing into the effectiveness of self-isolation policies in epidemic control

In this work, we inspect the reliability of controlling and quelling an epidemic disease mimicked by a susceptible–infected–susceptible (SIS) model defined on a complex network by means of current

Robustness of the Critical Behaviour in the Stochastic Greenberg-Hastings Cellular Automaton Model

It is shown that a continuous decrease of the probability of excitation of cells triggers a drastic change of behaviour, driving the system from an ‘active’ to an “extinct” steady state, and the position of the critical threshold can be predicted as it decreases linearly with the inverse of the average number of neighbours per cell.

Local persistence in the directed percolation universality class

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher

Bond percolation on simple cubic lattices with extended neighborhoods.

The results show that the percolation thresholds of these and other three-dimensional lattices decrease monotonically with the coordination number z quite accurately according to a power-law p_{c}∼z^{-a} with exponent a=1.111.



Epidemic spreading with immunization and mutations.

  • S. DammerH. Hinrichsen
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
A model that mimics epidemic spreading with immunization and mutations and shows that mutations lead generically to a crossover from the GEP to DP is introduced, and the protection gained by immunization is vitally decreased by the occurrence of mutations.

Generalized epidemic process and tricritical dynamic percolation.

The general epidemic process is generalized by introducing a fourth kind of individuals, viz., individuals which are weakened by the process but not yet infected, which gives rise to a mechanism that introduces a global instability in the spreading of the process and therefore opens the possibility of a discontinuous transition in addition to the usual continuous percolation transition.

Directed Percolation and Other Systems with Absorbing States

We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states.

Spatial Contact Models for Ecological and Epidemic Spread

A wide variety of phenomena of geographical spread can be described in terms of a mechanism of "growth" (e.g, birth, infection) and a "contact distribution" which describes how the locations of the

Phase Structure of Systems with Infinite Numbers of Absorbing States

Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to

Numerical studies of critical percolation in three dimensions

Presents results of high-statistics simulations of the spreading of 3D percolation close to the critical point. The main results are: (i) a more precise estimate of the spreading (resp. 'chemical

Epidemic models and percolation

The authors argue that local epidemic models with immunisation are in the same universality class as percolation cluster growth models, and show that the static exponents are equal to all orders in

Critical percolation in high dimensions.

  • P. Grassberger
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4-13 dimensions are presented and a scaling law for finite cluster size corrections is proposed.

Avalanche and spreading exponents in systems with absorbing states.

Using generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states, a collection of the state-of-the-art exponents for directed percolation, dynamical percolations, and other universality classes is presented.