Network-Based Epidemic Control Through Optimal Travel and Quarantine Management

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Swift global transmission of infectious diseases necessitates advanced control strategies.
• Existing models often lack comprehensive network-based optimization for epidemic containment.

Purpose of the Study:

• To develop and analyze a network-based framework for epidemic control.
• To investigate two distinct approaches: travel rate optimization and SIR model enhancement with quarantine.

Main Methods:

• Network optimization for reducing travel rates and analyzing convergence.
• Expanding the SIR model with optimized quarantined states, reducing it to matrix balancing.
• Utilizing augmented primal-dual gradient dynamics for optimal quarantine convergence.
• Validating models with public county-level data from Massachusetts.

Main Results:

• Travel rate reduction strategy effectiveness is dependent on network structure.
• The optimized quarantine problem links to matrix balancing and the epidemic's reproduction number.
• Augmented primal-dual gradient dynamics guarantee exponential convergence for quarantine optimization.
• Simulation studies confirm the practical applicability of the proposed framework.

Conclusions:

• Network structure is a critical factor in epidemic dynamics and control.
• Optimized travel reduction and quarantine strategies offer effective means to curb infectious disease spread.
• The developed framework provides a robust, data-driven approach to epidemic control.