Spreading processes with a unique absorbing state and finite lifetime of populations

TL;DR

This paper investigates how a finite population lifetime influences epidemic thresholds in processes with a unique absorbing state, demonstrating threshold-like behavior in long-term dynamics through theoretical analysis and simulations.

Contribution

It introduces the concept that finite population lifetime induces threshold-like behavior in epidemic processes with a unique absorbing state, extending understanding of epidemic dynamics.

Findings

Finite population lifetime leads to threshold-like behavior.

Long-term epidemic dynamics can be influenced by population lifetime.

Theoretical and simulation results support the threshold phenomenon.

Abstract

The presence of a unique absorbing state in the finite state space of an epidemic process always poses a challenge in the definition of its epidemiological threshold. Without the elimination of the absorbing state of the SIS process we show that an exponentially distributed finite lifetime of the population results in a threshold like beahivour in the long time limit. We illustrate our findings with the SIS dynamics on the complete graph and the star.