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

2022-02-01

IEEE Transactions on Circuits and Systems Part 1: Regular Papers

AI Summary

To address the neglect of individual protective behaviors and population mobility in existing epidemiological models during the COVID-19 pandemic, this paper proposes a dual-perspective stochastic SIRS model integrating micro-level behavioral heterogeneity with macro-level disease transmission. Methodologically, it introduces a *protection level*—a random variable capturing inter-individual variation in protective efficacy—and establishes an open Markovian queueing network to explicitly model inter-regional migration-driven epidemic spread. The key contributions are twofold: (i) the first incorporation of protection level as a stochastic parameter within the SIRS framework, and (ii) a novel open queueing network model grounded in migration dynamics, bridging the theoretical gap between individual behavior and population-level epidemiology. Through stochastic process analysis and Monte Carlo simulation, the study quantifies the suppression effect of protection level on infection probability, derives the steady-state distribution of population across disease states, and uncovers synergistic regulatory mechanisms whereby migration rate and protection intensity jointly govern epidemic peak magnitude and duration.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Security and Privacy: Large-scale security measurements

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.

Problem

• Modeling individual protection behaviors in epidemic propagation dynamics
• Analyzing population migration impacts through queueing network theory
• Investigating infection probability and state distribution in stochastic SIRS models

Innovation

• Individual protection degree as stochastic variable
• Open Markov queueing network for population dynamics
• Stochastic methods analyzing epidemic migration patterns