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Output-Feedback Control for Discrete-Time Spreading Models in Complex Networks.

Entropy (Basel, Switzerland)·2020
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Spreading Control in Two-Layer Multiplex Networks.

Roberto Bernal Jaquez1, Luis Angel Alarcón Ramos2, Alexander Schaum3

  • 1Department of Applied Mathematics and Systems, Universidad Autónoma Metropolitana, Cuajimalpa, Mexico-City 05348, Mexico.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary
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Controlling disease spread in multilayer networks is possible by adjusting transition rates. This study reveals how network structure impacts stability and control strategies for disease extinction.

Keywords:
multilayer complex networksspreading controlstability

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Area of Science:

  • Complex Networks
  • Epidemiology
  • Control Theory

Background:

  • Spreading processes in networks are crucial for understanding disease dynamics.
  • Controlling these processes in multilayer networks presents unique challenges compared to single-layer networks.
  • Achieving a stable extinction state is a key goal in epidemic control.

Purpose of the Study:

  • To address the control of spreading processes in two-layer multiplex networks to ensure the extinction state is a global attractor.
  • To analyze the stabilization of the extinction state in a Markov-chain based susceptible-infected-susceptible (SIS) dynamics model.
  • To investigate the impact of network structure on stability criteria and control requirements.

Main Methods:

  • Formulation of the problem using a Markov-chain based susceptible-infected-susceptible (SIS) dynamics.
  • Analysis of the nonlinear discrete-time model using dominant linear dynamics for global stability results.
  • Mathematical analysis, statistical evaluations, and simulation studies to verify findings.

Main Results:

  • Identified essential changes in stability criteria when moving from single to multilayer networks.
  • Determined the number of nodes requiring control intervention for stabilization.
  • Demonstrated that appropriate adaptation of transition rates can induce stability in multilayer networks.

Conclusions:

  • The extinction state in two-layer multiplex networks can be stabilized through parameter adaptation.
  • Understanding multilayer network properties is crucial for effective epidemic control strategies.
  • Control strategies need to account for inter-layer dynamics and network topology.