Self-driven criticality in a stochastic epidemic model

TL;DR

This paper introduces a stochastic epidemic model where the disease spread self-organizes into a critical state with reproduction rates near one, leading to prolonged epidemics, and analyzes its stability through numerical and analytical methods.

Contribution

The paper proposes a novel stochastic epidemic model demonstrating self-driven criticality, extending understanding of epidemic dynamics with heavy-tailed infection rate fluctuations.

Findings

The epidemic self-organizes into a critical state with reproduction rate near one.

The model predicts prolonged epidemics due to criticality.

Stability of the critical regime is confirmed analytically and numerically.

Abstract

We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective reproduction rate fluctuates close to the critical value one, as observed for different epidemics. The main assumptions underlying the model are that the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The critical regime is characterized by an extremely long duration of the epidemic. Its stability is analyzed both numerically and analytically.