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Epidemic processes with immunization.

Andrea Jiménez-Dalmaroni1, Haye Hinrichsen

  • 1Department of Physics-Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom. jimenez@thphys.ox.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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We investigated directed percolation (DP) with immunization, finding survival probability deviates from power-law behavior. This study explores critical dynamics under varying infection rates, confirmed by simulations.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Dynamical Systems

Background:

  • Directed Percolation (DP) models critical phenomena in systems with quenched disorder.
  • Immunization introduces distinct probabilities for initial and subsequent infections, altering system dynamics.
  • Non-Markovian effects arise from immunization, deviating from standard DP models.

Purpose of the Study:

  • To analyze the dynamical critical behavior of a directed percolation model with immunization.
  • To investigate the impact of varying first-infection rates on system survival probability.
  • To determine if survival probability follows power-law behavior under immunization effects.

Main Methods:

  • Field theoretical analysis incorporating a non-Markovian term due to immunization.

Related Experiment Videos

  • Perturbation theory around the DP fixed point in dimensions d<6.
  • Scaling arguments to derive survival probability expressions in low and high first-infection rate limits.
  • Optimized numerical simulations in 1+1 dimensions for validation.

    • Main Results:

    • Immunization drives the system away from the standard DP critical point.
    • Survival probability exhibits stretched exponential decay at low first-infection rates.
    • Survival probability converges to a constant at high first-infection rates.
    • Theoretical predictions align with numerical simulation results.

    Conclusions:

    • The survival probability in immunized DP does not follow a simple power-law.
    • Immunization significantly alters the critical dynamics and long-term behavior of DP systems.
    • The study provides a theoretical and numerical framework for understanding non-Markovian effects in critical phenomena.