Epidemic processes with immunization

Abstract

We study a model of directed percolation (DP) with immunization, i.e. with different probabilities for the first infection and subsequent infections. The immunization effect leads to an additional non-Markovian term in the corresponding field theoretical action. We consider immunization as a small perturbation around the DP fixed point in d<6, where the non-Markovian term is relevant. The immunization causes the system to be driven away from the neighbourhood of the DP critical point. In order to investigate the dynamical critical behaviour of the model, we consider the limits of low and high first infection rate, while the second infection rate remains constant at the DP critical value. Scaling arguments are applied to obtain an expression for the survival probability in both limits. The corresponding exponents are written in terms of the critical exponents for ordinary DP and DP with a wall. We find that the survival probability does not obey a power law behaviour, decaying instead as a stretched exponential in the low first infection probability limit and to a constant in the high first infection probability limit. The theoretical predictions are confirmed by optimized numerical simulations in 1+1 dimensions.

12 pages, 11 figures. v.2: minor corrections

References in corpus (2)

• Critical exponents of directed percolation measured in spatiotemporal intermittency
• Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states

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• Local Persistence in the Directed Percolation Universality Class
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• The true reinforced random walk with bias
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Three different routes from the directed Ising to the directed percolation class
• Directed percolation with incubation times
• Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
• Critical behavior of the diffusive susceptible-infected-recovered model
• Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities
• Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring