Phase Disorder Effects in a Cellular Automaton Model of Epidemic Propagation

TL;DR

This paper investigates how phase disorder influences epidemic spread in a cellular automaton model, revealing effects on propagation velocity, pattern formation, and transition to turbulence.

Contribution

It introduces a phase-disorder parameter into a cellular automaton epidemic model, demonstrating its impact on dynamical regimes and spatial infection patterns.

Findings

Phase-disorder prevents finite-velocity spreading of perturbations.

Increased phase-disorder leads to loss of ordered patterns and turbulence.

Phase-disorder can induce spatial isotropy in infection propagation.

Abstract

A deterministic cellular automaton rule defined on the Moore neighbourhood is studied as a model of epidemic propagation. The directed nature of the interaction between cells allows one to introduce the dependence on a disorder parameter that determines the fraction of ``in-phase'' cells. Phase-disorder is shown to produce peculiar changes in the dynamical and statistical properties of the different evolution regimes obtained by varying the infection and the immunization periods. In particular, the finite-velocity spreading of perturbations, characterizing chaotic evolution, can be prevented by localization effects induced by phase-disorder, that may also yield spatial isotropy of the infection propagation as a statistical effect. Analogously, the structure of phase-synchronous ordered patterns is rapidly lost as soon as phase-disorder is increased, yielding a defect-mediated turbulent regime.