Sudden spreading of infections in an epidemic model with a finite seed fraction

TL;DR

This paper investigates how a finite initial seed fraction influences epidemic spreading in a susceptible-weakened-infected-removed model on regular random graphs, revealing two critical infection rates and sudden epidemic transitions.

Contribution

It introduces the analysis of epidemic dynamics with a finite seed fraction, identifying two critical points and the conditions for abrupt epidemic spreading.

Findings

Two critical infection rates identified for finite seed scenarios.

Sudden epidemic spreading occurs at high network degrees with small seed fractions.

Percolation transition of removed nodes precedes the giant cluster growth.

Abstract

We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.