Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Abstract

a b s t r a c tWe investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters.

The evolution of COVID-19: A discontinuous approach

“…In this context, the question to treat in the biomedical research is if the abrupt transitions observed in the COVID-19 pandemic event can reflect the changes in the topological mode of disease progression. This is in line with studies dealing with the application of statistical–mechanical analogies on the space propagation of diseases [35] and the small-worlds [36] , [37] and fractal [38] modelling of epidemic processes [20] . Under this view, the first step of exponential growth corresponds to a small-worlds type of close vicinity contact.…”

Epidemic Dynamics in Open Quantum Spin Systems

“…Performing the same finite size scaling analysis of Ref. [36] we have first derived the critical value of the control parameter α c (L) (setting κ = 1 for simplicity) by locating the maximum of the numerical derivative of the order parameter N SS with respect to α or, in other words, the inflection point of the curve, where it switches from being convex to concave. In the thermodynamic limit L → ∞, this point will approach the actual critical value α c , where a non-analiticity develops, signalling the presence of a second order phase transition.…”

Recursive contact tracing in Reed-Frost epidemic models

“…In Section III, we perform a numerical study of the Reed-Frost model with recursive contact tracing on the square lattice. We present evidence for a contact-tracing phase transition on the square lattice as N → ∞, whose finite-size scaling near the critical line lies in the universality class of two-dimensional percolation [16,[20][21][22]. As for the Bethe lattice [14], we find that the critical line connects smoothly to the singular point of perfect contact tracing and purely asymptomatic transmission, where universal behaviour gives way to a discontinuous phase transition.…”

“…For concreteness, let us focus on the square lattice, for which d = 2 < d c . Previous works have established that the critical SIR model on the square lattice lies in the same universality class as two-dimensional percolation [20][21][22]. A natural question is whether the qualitative renormalization group argument above extends to the square lattice, i.e.…”