Protection Degree and Migration in the Stochastic SIRS Model: A Queueing System Perspective

TL;DR

This paper introduces stochastic models incorporating individual protection and migration into the SIRS epidemic framework, using queueing theory to analyze epidemic dynamics and effects of behaviors on disease spread.

Contribution

It proposes novel stochastic models that integrate protection levels and migration, providing a new perspective on epidemic modeling with queueing systems.

Findings

Protection degree reduces epidemic levels in simulations.

Migration influences the distribution of epidemic states.

Models accurately predict infection probabilities and population states.

Abstract

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated.