Epidemic spreading with long-range infections and incubation times

TL;DR

This paper investigates epidemic spreading models with long-range infections and incubation times, revealing a phase transition characterized by varying critical exponents, bridging mean-field and directed percolation universality classes.

Contribution

It introduces a combined field-theoretical and numerical analysis of epidemic models with algebraically decaying spreading distances and incubation times, extending understanding of critical behavior.

Findings

Critical exponents vary continuously across the phase transition.

The transition belongs to a universality class extending directed percolation.

Numerical simulations confirm theoretical predictions in one dimension.

Abstract

The non-equilibrium phase transition in models for epidemic spreading with long-range infections in combination with incubation times is investigated by field-theoretical and numerical methods. Here the spreading process is modelled by spatio-temporal Levy flights, i.e., it is assumed that both spreading distance and incubation time decay algebraically. Depending on the infection rate one observes a phase transition from a fluctuating active phase into an absorbing phase, where the infection becomes extinct. This transition between spreading and extinction is characterized by continuously varying critical exponents, extending from a mean-field regime to a phase described by the universality class of directed percolation. We compute the critical exponents in the vicinity of the upper critical dimension by a field-theoretic renormalization group calculation and verify the results in one spatial dimension by extensive numerical simulations.