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SIR Dynamics with Vaccination in a Large Configuration Model.

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This study analyzes an SIR model with vaccination on random graphs, revealing how network structure impacts epidemic control. Optimal vaccination strategies are derived using game theory, demonstrating reduced infections and highlighting network influence.

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Configuration modelEpidemicOptimal controlSIR-V

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Epidemic modeling is crucial for public health interventions.
  • Understanding disease spread on complex networks requires advanced mathematical frameworks.
  • Vaccination strategies are key to controlling infectious diseases.

Purpose of the Study:

  • To analyze an SIR model with vaccination on sparse random graphs.
  • To investigate the influence of graph characteristics on vaccination efficiency.
  • To derive optimal vaccination controls in centralized and decentralized settings.

Main Methods:

  • Utilizing a configuration model random graph framework.
  • Applying game theory to formulate and solve optimal control problems.
  • Analyzing system convergence and scaling limits for large networks.
  • Conducting simulations to evaluate vaccination strategies.

Main Results:

  • Demonstrated convergence and characterized scaling limits of the SIR model on random graphs.
  • Proved the existence of optimal controls for vaccination strategies.
  • Quantified the impact of degree distribution on vaccination efficiency and final epidemic size.
  • Simulations showed optimal controls reduce infections, emphasizing network role.

Conclusions:

  • Network characteristics significantly influence epidemic propagation and vaccination program effectiveness.
  • Optimal control strategies, informed by graph properties, can minimize disease spread.
  • Game theory provides a robust framework for designing vaccination policies in complex networks.