Transient Analysis of a Resource-limited Recovery Policy for Epidemics: a Retrial Queueing Approach

TL;DR

This paper models the transient dynamics of an epidemic process using a retrial queueing system, providing insights into how recovery policies and contact heterogeneity influence epidemic spread over time.

Contribution

It introduces a novel stochastic SI epidemic model with a retrial queueing approach, analyzing transient behavior through Laplace transforms of state probabilities.

Findings

Heterogeneity in contacts significantly affects epidemic dynamics.

Retrial frequency impacts recovery effectiveness and epidemic duration.

Transient state probabilities are derived for both homogeneous and heterogeneous contact scenarios.

Abstract

Knowledge on the dynamics of standard epidemic models and their variants over complex networks has been well-established primarily in the stationary regime, with relatively little light shed on their transient behavior. In this paper, we analyze the transient characteristics of the classical susceptible-infected (SI) process with a recovery policy modeled as a state-dependent retrial queueing system in which arriving infected nodes, upon finding all the limited number of recovery units busy, join a virtual buffer and try persistently for service in order to regain susceptibility. In particular, we formulate the stochastic SI epidemic model with added retrial phenomenon as a finite continuous-time Markov chain (CTMC) and derive the Laplace transforms of the underlying transient state probability distributions and corresponding moments for a closed population of size $N$ driven by homogeneous and heterogeneous contacts. Our numerical results reveal the strong influence of infection heterogeneity and retrial frequency on the transient behavior of the model for various performance measures.